论坛 › 难题征解 › 连分数的难题

markfang2050 发表于 2019-9-19 21:22:40

连分数的难题

如图，不限制自然数范围，求出所有解（集合，不排序）的个数。

.·.·. 发表于 2019-9-20 12:52:08

如果是6个不同的，没记错第一个一定是1/2
然后剩下的搜就是了
坛子里有搜的方法与理论

如果约定前面的分母比后面的小，那么，当前面k个分母给定之后，后面的分数之和的上界也就给定了
我们可以借助这个上界划定搜索范围

然后剩下的就是搜了

zeroieme 发表于 2019-9-20 13:08:07

不是连分数，这个叫埃及分数。

mathe 发表于 2019-9-20 13:30:18

https://bbs.emath.ac.cn/thread-223-2-1.html

mathe 发表于 2019-9-20 15:28:12

计算结果好像2320组解
比如有
1/2 +1/3 +1/7 +1/43 +1/1807 +1/3263442
1/2 +1/3 +1/7 +1/43 +1/1808 +1/1632624
1/2 +1/3 +1/7 +1/43 +1/1809 +1/1089018
1/2 +1/3 +1/7 +1/43 +1/1810 +1/817215
1/2 +1/3 +1/7 +1/43 +1/1812 +1/545412
1/2 +1/3 +1/7 +1/43 +1/1813 +1/467754
1/2 +1/3 +1/7 +1/43 +1/1815 +1/364210
1/2 +1/3 +1/7 +1/43 +1/1818 +1/273609
1/2 +1/3 +1/7 +1/43 +1/1820 +1/234780
1/2 +1/3 +1/7 +1/43 +1/1824 +1/183008
1/2 +1/3 +1/7 +1/43 +1/1827 +1/157122
1/2 +1/3 +1/7 +1/43 +1/1834 +1/118293
1/2 +1/3 +1/7 +1/43 +1/1842 +1/92407
...
1/3 +1/4 +1/5 +1/9 +1/18 +1/20
1/3 +1/4 +1/5 +1/10 +1/12 +1/30
1/3 +1/4 +1/5 +1/10 +1/15 +1/20
1/3 +1/4 +1/6 +1/7 +1/10 +1/140
1/3 +1/4 +1/6 +1/7 +1/12 +1/42
1/3 +1/4 +1/6 +1/7 +1/14 +1/28
1/3 +1/4 +1/6 +1/8 +1/9 +1/72
1/3 +1/4 +1/6 +1/8 +1/10 +1/40
1/3 +1/4 +1/6 +1/8 +1/12 +1/24
1/3 +1/4 +1/6 +1/9 +1/12 +1/18
1/3 +1/4 +1/6 +1/10 +1/12 +1/15

markfang2050 发表于 2019-9-20 16:01:27

mathe 发表于 2019-9-20 15:28
计算结果好像2320组解
比如有
1/2 +1/3 +1/7 +1/43 +1/1807 +1/3263442


2320是对的。MMA验证过。你的程序能否发下看看？

markfang2050 发表于 2019-9-20 19:56:14

{{2, 3, 7, 43, 1807, 3263442}, {2, 3, 7, 43, 1808, 1632624}, {2, 3, 7,
    43, 1809, 1089018}, {2, 3, 7, 43, 1810, 817215}, {2, 3, 7, 43,
   1812, 545412}, {2, 3, 7, 43, 1813, 467754}, {2, 3, 7, 43, 1815,
   364210}, {2, 3, 7, 43, 1818, 273609}, {2, 3, 7, 43, 1820,
   234780}, {2, 3, 7, 43, 1824, 183008}, {2, 3, 7, 43, 1827,
   157122}, {2, 3, 7, 43, 1834, 118293}, {2, 3, 7, 43, 1842,
   92407}, {2, 3, 7, 43, 1848, 79464}, {2, 3, 7, 43, 1849, 77658}, {2,
    3, 7, 43, 1855, 68370}, {2, 3, 7, 43, 1869, 53578}, {2, 3, 7, 43,
   1890, 40635}, {2, 3, 7, 43, 1892, 39732}, {2, 3, 7, 43, 1904,
   35088}, {2, 3, 7, 43, 1932, 27692}, {2, 3, 7, 43, 1935, 27090}, {2,
    3, 7, 43, 1953, 23994}, {2, 3, 7, 43, 1978, 20769}, {2, 3, 7, 43,
   2002, 18447}, {2, 3, 7, 43, 2058, 14749}, {2, 3, 7, 43, 2064,
   14448}, {2, 3, 7, 43, 2100, 12900}, {2, 3, 7, 43, 2107, 12642}, {2,
    3, 7, 43, 2193, 10234}, {2, 3, 7, 43, 2247, 9202}, {2, 3, 7, 43,
   2322, 8127}, {2, 3, 7, 43, 2394, 7353}, {2, 3, 7, 43, 2408,
   7224}, {2, 3, 7, 43, 2580, 6020}, {2, 3, 7, 43, 2688, 5504}, {2, 3,
    7, 43, 2709, 5418}, {2, 3, 7, 43, 3010, 4515}, {2, 3, 7, 43, 3354,
    3913}, {2, 3, 7, 43, 3570, 3655}, {2, 3, 7, 44, 925, 854700}, {2,
   3, 7, 44, 926, 427812}, {2, 3, 7, 44, 927, 285516}, {2, 3, 7, 44,
   928, 214368}, {2, 3, 7, 44, 930, 143220}, {2, 3, 7, 44, 931,
   122892}, {2, 3, 7, 44, 932, 107646}, {2, 3, 7, 44, 933, 95788}, {2,
    3, 7, 44, 935, 78540}, {2, 3, 7, 44, 936, 72072}, {2, 3, 7, 44,
   938, 61908}, {2, 3, 7, 44, 940, 54285}, {2, 3, 7, 44, 942,
   48356}, {2, 3, 7, 44, 945, 41580}, {2, 3, 7, 44, 946, 39732}, {2,
   3, 7, 44, 948, 36498}, {2, 3, 7, 44, 952, 31416}, {2, 3, 7, 44,
   957, 26796}, {2, 3, 7, 44, 960, 24640}, {2, 3, 7, 44, 966,
   21252}, {2, 3, 7, 44, 968, 20328}, {2, 3, 7, 44, 972, 18711}, {2,
   3, 7, 44, 973, 18348}, {2, 3, 7, 44, 980, 16170}, {2, 3, 7, 44,
   987, 14476}, {2, 3, 7, 44, 990, 13860}, {2, 3, 7, 44, 996,
   12782}, {2, 3, 7, 44, 1001, 12012}, {2, 3, 7, 44, 1008, 11088}, {2,
    3, 7, 44, 1012, 10626}, {2, 3, 7, 44, 1022, 9636}, {2, 3, 7, 44,
   1023, 9548}, {2, 3, 7, 44, 1036, 8547}, {2, 3, 7, 44, 1045,
   7980}, {2, 3, 7, 44, 1050, 7700}, {2, 3, 7, 44, 1056, 7392}, {2, 3,
    7, 44, 1068, 6853}, {2, 3, 7, 44, 1071, 6732}, {2, 3, 7, 44, 1078,
    6468}, {2, 3, 7, 44, 1092, 6006}, {2, 3, 7, 44, 1100, 5775}, {2,
   3, 7, 44, 1120, 5280}, {2, 3, 7, 44, 1122, 5236}, {2, 3, 7, 44,
   1155, 4620}, {2, 3, 7, 44, 1166, 4452}, {2, 3, 7, 44, 1176,
   4312}, {2, 3, 7, 44, 1188, 4158}, {2, 3, 7, 44, 1218, 3828}, {2, 3,
    7, 44, 1232, 3696}, {2, 3, 7, 44, 1260, 3465}, {2, 3, 7, 44, 1287,
    3276}, {2, 3, 7, 44, 1316, 3102}, {2, 3, 7, 44, 1320, 3080}, {2,
   3, 7, 44, 1365, 2860}, {2, 3, 7, 44, 1386, 2772}, {2, 3, 7, 44,
   1408, 2688}, {2, 3, 7, 44, 1428, 2618}, {2, 3, 7, 44, 1452,
   2541}, {2, 3, 7, 44, 1463, 2508}, {2, 3, 7, 44, 1512, 2376}, {2, 3,
    7, 44, 1540, 2310}, {2, 3, 7, 44, 1617, 2156}, {2, 3, 7, 44, 1650,
    2100}, {2, 3, 7, 44, 1708, 2013}, {2, 3, 7, 44, 1716, 2002}, {2,
   3, 7, 44, 1771, 1932}, {2, 3, 7, 44, 1806, 1892}, {2, 3, 7, 45,
   631, 397530}, {2, 3, 7, 45, 632, 199080}, {2, 3, 7, 45, 633,
   132930}, {2, 3, 7, 45, 634, 99855}, {2, 3, 7, 45, 635, 80010}, {2,
   3, 7, 45, 636, 66780}, {2, 3, 7, 45, 637, 57330}, {2, 3, 7, 45,
   639, 44730}, {2, 3, 7, 45, 640, 40320}, {2, 3, 7, 45, 642,
   33705}, {2, 3, 7, 45, 644, 28980}, {2, 3, 7, 45, 645, 27090}, {2,
   3, 7, 45, 648, 22680}, {2, 3, 7, 45, 650, 20475}, {2, 3, 7, 45,
   651, 19530}, {2, 3, 7, 45, 655, 16506}, {2, 3, 7, 45, 657,
   15330}, {2, 3, 7, 45, 658, 14805}, {2, 3, 7, 45, 660, 13860}, {2,
   3, 7, 45, 665, 11970}, {2, 3, 7, 45, 666, 11655}, {2, 3, 7, 45,
   672, 10080}, {2, 3, 7, 45, 675, 9450}, {2, 3, 7, 45, 679,
   8730}, {2, 3, 7, 45, 680, 8568}, {2, 3, 7, 45, 684, 7980}, {2, 3,
   7, 45, 690, 7245}, {2, 3, 7, 45, 693, 6930}, {2, 3, 7, 45, 700,
   6300}, {2, 3, 7, 45, 705, 5922}, {2, 3, 7, 45, 711, 5530}, {2, 3,
   7, 45, 714, 5355}, {2, 3, 7, 45, 720, 5040}, {2, 3, 7, 45, 728,
   4680}, {2, 3, 7, 45, 730, 4599}, {2, 3, 7, 45, 735, 4410}, {2, 3,
   7, 45, 738, 4305}, {2, 3, 7, 45, 756, 3780}, {2, 3, 7, 45, 765,
   3570}, {2, 3, 7, 45, 770, 3465}, {2, 3, 7, 45, 777, 3330}, {2, 3,
   7, 45, 780, 3276}, {2, 3, 7, 45, 792, 3080}, {2, 3, 7, 45, 805,
   2898}, {2, 3, 7, 45, 810, 2835}, {2, 3, 7, 45, 819, 2730}, {2, 3,
   7, 45, 826, 2655}, {2, 3, 7, 45, 840, 2520}, {2, 3, 7, 45, 855,
   2394}, {2, 3, 7, 45, 875, 2250}, {2, 3, 7, 45, 882, 2205}, {2, 3,
   7, 45, 900, 2100}, {2, 3, 7, 45, 924, 1980}, {2, 3, 7, 45, 930,
   1953}, {2, 3, 7, 45, 945, 1890}, {2, 3, 7, 45, 954, 1855}, {2, 3,
   7, 45, 980, 1764}, {2, 3, 7, 45, 1008, 1680}, {2, 3, 7, 45, 1035,
   1610}, {2, 3, 7, 45, 1050, 1575}, {2, 3, 7, 45, 1071, 1530}, {2, 3,
    7, 45, 1080, 1512}, {2, 3, 7, 45, 1120, 1440}, {2, 3, 7, 45, 1155,
    1386}, {2, 3, 7, 45, 1170, 1365}, {2, 3, 7, 45, 1197, 1330}, {2,
   3, 7, 45, 1218, 1305}, {2, 3, 7, 46, 484, 233772}, {2, 3, 7, 46,
   486, 78246}, {2, 3, 7, 46, 490, 33810}, {2, 3, 7, 46, 492,
   26404}, {2, 3, 7, 46, 504, 11592}, {2, 3, 7, 46, 506, 10626}, {2,
   3, 7, 46, 532, 5244}, {2, 3, 7, 46, 546, 4186}, {2, 3, 7, 46, 552,
   3864}, {2, 3, 7, 46, 630, 2070}, {2, 3, 7, 46, 644, 1932}, {2, 3,
   7, 46, 690, 1610}, {2, 3, 7, 46, 924, 1012}, {2, 3, 7, 47, 395,
   779730}, {2, 3, 7, 47, 396, 130284}, {2, 3, 7, 47, 399, 37506}, {2,
    3, 7, 47, 402, 22043}, {2, 3, 7, 47, 420, 6580}, {2, 3, 7, 47,
   423, 5922}, {2, 3, 7, 47, 434, 4371}, {2, 3, 7, 47, 483, 2162}, {2,
    3, 7, 47, 564, 1316}, {2, 3, 7, 47, 658, 987}, {2, 3, 7, 48, 337,
   113232}, {2, 3, 7, 48, 338, 56784}, {2, 3, 7, 48, 339, 37968}, {2,
   3, 7, 48, 340, 28560}, {2, 3, 7, 48, 342, 19152}, {2, 3, 7, 48,
   343, 16464}, {2, 3, 7, 48, 344, 14448}, {2, 3, 7, 48, 345,
   12880}, {2, 3, 7, 48, 348, 9744}, {2, 3, 7, 48, 350, 8400}, {2, 3,
   7, 48, 352, 7392}, {2, 3, 7, 48, 354, 6608}, {2, 3, 7, 48, 357,
   5712}, {2, 3, 7, 48, 360, 5040}, {2, 3, 7, 48, 364, 4368}, {2, 3,
   7, 48, 368, 3864}, {2, 3, 7, 48, 372, 3472}, {2, 3, 7, 48, 378,
   3024}, {2, 3, 7, 48, 384, 2688}, {2, 3, 7, 48, 385, 2640}, {2, 3,
   7, 48, 392, 2352}, {2, 3, 7, 48, 399, 2128}, {2, 3, 7, 48, 400,
   2100}, {2, 3, 7, 48, 408, 1904}, {2, 3, 7, 48, 420, 1680}, {2, 3,
   7, 48, 432, 1512}, {2, 3, 7, 48, 434, 1488}, {2, 3, 7, 48, 448,
   1344}, {2, 3, 7, 48, 462, 1232}, {2, 3, 7, 48, 464, 1218}, {2, 3,
   7, 48, 480, 1120}, {2, 3, 7, 48, 483, 1104}, {2, 3, 7, 48, 504,
   1008}, {2, 3, 7, 48, 528, 924}, {2, 3, 7, 48, 532, 912}, {2, 3, 7,
   48, 560, 840}, {2, 3, 7, 48, 588, 784}, {2, 3, 7, 48, 592,
   777}, {2, 3, 7, 48, 624, 728}, {2, 3, 7, 48, 630, 720}, {2, 3, 7,
   49, 295, 86730}, {2, 3, 7, 49, 296, 43512}, {2, 3, 7, 49, 297,
   29106}, {2, 3, 7, 49, 298, 21903}, {2, 3, 7, 49, 300, 14700}, {2,
   3, 7, 49, 301, 12642}, {2, 3, 7, 49, 303, 9898}, {2, 3, 7, 49, 306,
    7497}, {2, 3, 7, 49, 308, 6468}, {2, 3, 7, 49, 312, 5096}, {2, 3,
   7, 49, 315, 4410}, {2, 3, 7, 49, 322, 3381}, {2, 3, 7, 49, 330,
   2695}, {2, 3, 7, 49, 336, 2352}, {2, 3, 7, 49, 343, 2058}, {2, 3,
   7, 49, 357, 1666}, {2, 3, 7, 49, 378, 1323}, {2, 3, 7, 49, 392,
   1176}, {2, 3, 7, 49, 420, 980}, {2, 3, 7, 49, 441, 882}, {2, 3, 7,
   49, 490, 735}, {2, 3, 7, 49, 546, 637}, {2, 3, 7, 50, 263,
   138075}, {2, 3, 7, 50, 264, 46200}, {2, 3, 7, 50, 265, 27825}, {2,
   3, 7, 50, 266, 19950}, {2, 3, 7, 50, 267, 15575}, {2, 3, 7, 50,
   270, 9450}, {2, 3, 7, 50, 273, 6825}, {2, 3, 7, 50, 275, 5775}, {2,
    3, 7, 50, 280, 4200}, {2, 3, 7, 50, 285, 3325}, {2, 3, 7, 50, 287,
    3075}, {2, 3, 7, 50, 294, 2450}, {2, 3, 7, 50, 300, 2100}, {2, 3,
   7, 50, 315, 1575}, {2, 3, 7, 50, 325, 1365}, {2, 3, 7, 50, 336,
   1200}, {2, 3, 7, 50, 350, 1050}, {2, 3, 7, 50, 375, 875}, {2, 3, 7,
    50, 385, 825}, {2, 3, 7, 50, 420, 700}, {2, 3, 7, 50, 450,
   630}, {2, 3, 7, 50, 483, 575}, {2, 3, 7, 51, 239, 56882}, {2, 3, 7,
    51, 240, 28560}, {2, 3, 7, 51, 242, 14399}, {2, 3, 7, 51, 245,
   8330}, {2, 3, 7, 51, 252, 4284}, {2, 3, 7, 51, 255, 3570}, {2, 3,
   7, 51, 266, 2261}, {2, 3, 7, 51, 272, 1904}, {2, 3, 7, 51, 287,
   1394}, {2, 3, 7, 51, 306, 1071}, {2, 3, 7, 51, 336, 816}, {2, 3, 7,
    51, 357, 714}, {2, 3, 7, 51, 434, 527}, {2, 3, 7, 52, 219,
   79716}, {2, 3, 7, 52, 220, 30030}, {2, 3, 7, 52, 221, 18564}, {2,
   3, 7, 52, 222, 13468}, {2, 3, 7, 52, 224, 8736}, {2, 3, 7, 52, 228,
    5187}, {2, 3, 7, 52, 231, 4004}, {2, 3, 7, 52, 234, 3276}, {2, 3,
   7, 52, 238, 2652}, {2, 3, 7, 52, 252, 1638}, {2, 3, 7, 52, 260,
   1365}, {2, 3, 7, 52, 273, 1092}, {2, 3, 7, 52, 286, 924}, {2, 3, 7,
    52, 312, 728}, {2, 3, 7, 52, 336, 624}, {2, 3, 7, 52, 364,
   546}, {2, 3, 7, 52, 420, 455}, {2, 3, 7, 53, 203, 64554}, {2, 3, 7,
    53, 204, 25228}, {2, 3, 7, 53, 210, 5565}, {2, 3, 7, 53, 212,
   4452}, {2, 3, 7, 54, 190, 35910}, {2, 3, 7, 54, 192, 12096}, {2, 3,
    7, 54, 196, 5292}, {2, 3, 7, 54, 198, 4158}, {2, 3, 7, 54, 210,
   1890}, {2, 3, 7, 54, 216, 1512}, {2, 3, 7, 54, 238, 918}, {2, 3, 7,
    54, 252, 756}, {2, 3, 7, 54, 270, 630}, {2, 3, 7, 54, 336,
   432}, {2, 3, 7, 55, 178, 102795}, {2, 3, 7, 55, 180, 13860}, {2, 3,
    7, 55, 187, 3570}, {2, 3, 7, 55, 189, 2970}, {2, 3, 7, 55, 195,
   2002}, {2, 3, 7, 55, 210, 1155}, {2, 3, 7, 55, 220, 924}, {2, 3, 7,
    55, 231, 770}, {2, 3, 7, 55, 308, 420}, {2, 3, 7, 55, 330,
   385}, {2, 3, 7, 56, 169, 28392}, {2, 3, 7, 56, 170, 14280}, {2, 3,
   7, 56, 171, 9576}, {2, 3, 7, 56, 172, 7224}, {2, 3, 7, 56, 174,
   4872}, {2, 3, 7, 56, 175, 4200}, {2, 3, 7, 56, 176, 3696}, {2, 3,
   7, 56, 177, 3304}, {2, 3, 7, 56, 180, 2520}, {2, 3, 7, 56, 182,
   2184}, {2, 3, 7, 56, 184, 1932}, {2, 3, 7, 56, 186, 1736}, {2, 3,
   7, 56, 189, 1512}, {2, 3, 7, 56, 192, 1344}, {2, 3, 7, 56, 196,
   1176}, {2, 3, 7, 56, 200, 1050}, {2, 3, 7, 56, 204, 952}, {2, 3, 7,
    56, 210, 840}, {2, 3, 7, 56, 216, 756}, {2, 3, 7, 56, 217,
   744}, {2, 3, 7, 56, 224, 672}, {2, 3, 7, 56, 231, 616}, {2, 3, 7,
   56, 232, 609}, {2, 3, 7, 56, 240, 560}, {2, 3, 7, 56, 252,
   504}, {2, 3, 7, 56, 264, 462}, {2, 3, 7, 56, 266, 456}, {2, 3, 7,
   56, 280, 420}, {2, 3, 7, 56, 294, 392}, {2, 3, 7, 56, 312,
   364}, {2, 3, 7, 56, 315, 360}, {2, 3, 7, 57, 160, 63840}, {2, 3, 7,
    57, 161, 18354}, {2, 3, 7, 57, 162, 10773}, {2, 3, 7, 57, 168,
   3192}, {2, 3, 7, 57, 171, 2394}, {2, 3, 7, 57, 189, 1026}, {2, 3,
   7, 57, 210, 665}, {2, 3, 7, 57, 228, 532}, {2, 3, 7, 57, 266,
   399}, {2, 3, 7, 57, 304, 336}, {2, 3, 7, 58, 153, 31059}, {2, 3, 7,
    58, 154, 13398}, {2, 3, 7, 58, 168, 1624}, {2, 3, 7, 58, 174,
   1218}, {2, 3, 7, 58, 189, 783}, {2, 3, 7, 58, 203, 609}, {2, 3, 7,
   59, 146, 90447}, {2, 3, 7, 59, 147, 17346}, {2, 3, 7, 59, 177,
   826}, {2, 3, 7, 60, 141, 19740}, {2, 3, 7, 60, 142, 9940}, {2, 3,
   7, 60, 144, 5040}, {2, 3, 7, 60, 145, 4060}, {2, 3, 7, 60, 147,
   2940}, {2, 3, 7, 60, 148, 2590}, {2, 3, 7, 60, 150, 2100}, {2, 3,
   7, 60, 154, 1540}, {2, 3, 7, 60, 156, 1365}, {2, 3, 7, 60, 160,
   1120}, {2, 3, 7, 60, 165, 924}, {2, 3, 7, 60, 168, 840}, {2, 3, 7,
   60, 175, 700}, {2, 3, 7, 60, 180, 630}, {2, 3, 7, 60, 189,
   540}, {2, 3, 7, 60, 190, 532}, {2, 3, 7, 60, 196, 490}, {2, 3, 7,
   60, 210, 420}, {2, 3, 7, 60, 220, 385}, {2, 3, 7, 60, 238,
   340}, {2, 3, 7, 60, 240, 336}, {2, 3, 7, 60, 252, 315}, {2, 3, 7,
   61, 135, 115290}, {2, 3, 7, 61, 140, 3660}, {2, 3, 7, 62, 132,
   9548}, {2, 3, 7, 62, 140, 1860}, {2, 3, 7, 62, 186, 434}, {2, 3, 7,
    63, 127, 16002}, {2, 3, 7, 63, 128, 8064}, {2, 3, 7, 63, 129,
   5418}, {2, 3, 7, 63, 130, 4095}, {2, 3, 7, 63, 132, 2772}, {2, 3,
   7, 63, 133, 2394}, {2, 3, 7, 63, 135, 1890}, {2, 3, 7, 63, 138,
   1449}, {2, 3, 7, 63, 140, 1260}, {2, 3, 7, 63, 144, 1008}, {2, 3,
   7, 63, 147, 882}, {2, 3, 7, 63, 153, 714}, {2, 3, 7, 63, 154,
   693}, {2, 3, 7, 63, 162, 567}, {2, 3, 7, 63, 168, 504}, {2, 3, 7,
   63, 175, 450}, {2, 3, 7, 63, 180, 420}, {2, 3, 7, 63, 189,
   378}, {2, 3, 7, 63, 207, 322}, {2, 3, 7, 63, 210, 315}, {2, 3, 7,
   63, 224, 288}, {2, 3, 7, 63, 234, 273}, {2, 3, 7, 64, 123,
   18368}, {2, 3, 7, 64, 126, 4032}, {2, 3, 7, 64, 128, 2688}, {2, 3,
   7, 64, 140, 960}, {2, 3, 7, 64, 168, 448}, {2, 3, 7, 64, 192,
   336}, {2, 3, 7, 65, 119, 46410}, {2, 3, 7, 65, 120, 10920}, {2, 3,
   7, 65, 130, 1365}, {2, 3, 7, 65, 140, 780}, {2, 3, 7, 65, 210,
   273}, {2, 3, 7, 66, 116, 26796}, {2, 3, 7, 66, 117, 9009}, {2, 3,
   7, 66, 119, 3927}, {2, 3, 7, 66, 120, 3080}, {2, 3, 7, 66, 121,
   2541}, {2, 3, 7, 66, 126, 1386}, {2, 3, 7, 66, 132, 924}, {2, 3, 7,
    66, 140, 660}, {2, 3, 7, 66, 147, 539}, {2, 3, 7, 66, 154,
   462}, {2, 3, 7, 66, 165, 385}, {2, 3, 7, 66, 176, 336}, {2, 3, 7,
   66, 189, 297}, {2, 3, 7, 67, 114, 8911}, {2, 3, 7, 68, 110,
   78540}, {2, 3, 7, 68, 112, 5712}, {2, 3, 7, 68, 119, 1428}, {2, 3,
   7, 68, 140, 510}, {2, 3, 7, 68, 204, 238}, {2, 3, 7, 69, 108,
   17388}, {2, 3, 7, 69, 112, 2576}, {2, 3, 7, 69, 115, 1610}, {2, 3,
   7, 69, 138, 483}, {2, 3, 7, 69, 140, 460}, {2, 3, 7, 69, 161,
   322}, {2, 3, 7, 70, 106, 11130}, {2, 3, 7, 70, 108, 3780}, {2, 3,
   7, 70, 110, 2310}, {2, 3, 7, 70, 112, 1680}, {2, 3, 7, 70, 114,
   1330}, {2, 3, 7, 70, 120, 840}, {2, 3, 7, 70, 126, 630}, {2, 3, 7,
   70, 130, 546}, {2, 3, 7, 70, 140, 420}, {2, 3, 7, 70, 150,
   350}, {2, 3, 7, 70, 154, 330}, {2, 3, 7, 70, 168, 280}, {2, 3, 7,
   70, 180, 252}, {2, 3, 7, 71, 105, 4970}, {2, 3, 7, 72, 101,
   50904}, {2, 3, 7, 72, 102, 8568}, {2, 3, 7, 72, 104, 3276}, {2, 3,
   7, 72, 105, 2520}, {2, 3, 7, 72, 108, 1512}, {2, 3, 7, 72, 112,
   1008}, {2, 3, 7, 72, 117, 728}, {2, 3, 7, 72, 120, 630}, {2, 3, 7,
   72, 126, 504}, {2, 3, 7, 72, 140, 360}, {2, 3, 7, 72, 144,
   336}, {2, 3, 7, 72, 168, 252}, {2, 3, 7, 72, 189, 216}, {2, 3, 7,
   73, 99, 101178}, {2, 3, 7, 74, 98, 10878}, {2, 3, 7, 74, 105,
   1295}, {2, 3, 7, 74, 111, 777}, {2, 3, 7, 75, 96, 16800}, {2, 3, 7,
    75, 98, 3675}, {2, 3, 7, 75, 100, 2100}, {2, 3, 7, 75, 105,
   1050}, {2, 3, 7, 75, 140, 300}, {2, 3, 7, 75, 175, 210}, {2, 3, 7,
   76, 94, 75012}, {2, 3, 7, 76, 95, 7980}, {2, 3, 7, 76, 96,
   4256}, {2, 3, 7, 76, 114, 532}, {2, 3, 7, 76, 140, 285}, {2, 3, 7,
   77, 93, 14322}, {2, 3, 7, 77, 96, 2464}, {2, 3, 7, 77, 98,
   1617}, {2, 3, 7, 77, 99, 1386}, {2, 3, 7, 77, 105, 770}, {2, 3, 7,
   77, 112, 528}, {2, 3, 7, 77, 132, 308}, {2, 3, 7, 77, 154,
   231}, {2, 3, 7, 77, 165, 210}, {2, 3, 7, 78, 92, 8372}, {2, 3, 7,
   78, 98, 1274}, {2, 3, 7, 78, 104, 728}, {2, 3, 7, 78, 140,
   260}, {2, 3, 7, 79, 90, 24885}, {2, 3, 7, 79, 91, 6162}, {2, 3, 7,
   80, 90, 5040}, {2, 3, 7, 80, 91, 3120}, {2, 3, 7, 80, 96,
   1120}, {2, 3, 7, 80, 105, 560}, {2, 3, 7, 80, 112, 420}, {2, 3, 7,
   80, 120, 336}, {2, 3, 7, 80, 140, 240}, {2, 3, 7, 81, 90,
   2835}, {2, 3, 7, 81, 91, 2106}, {2, 3, 7, 81, 162, 189}, {2, 3, 7,
   82, 87, 8323}, {2, 3, 7, 82, 91, 1599}, {2, 3, 7, 82, 123,
   287}, {2, 3, 7, 84, 85, 7140}, {2, 3, 7, 84, 86, 3612}, {2, 3, 7,
   84, 87, 2436}, {2, 3, 7, 84, 88, 1848}, {2, 3, 7, 84, 90,
   1260}, {2, 3, 7, 84, 91, 1092}, {2, 3, 7, 84, 92, 966}, {2, 3, 7,
   84, 93, 868}, {2, 3, 7, 84, 96, 672}, {2, 3, 7, 84, 98, 588}, {2,
   3, 7, 84, 100, 525}, {2, 3, 7, 84, 102, 476}, {2, 3, 7, 84, 105,
   420}, {2, 3, 7, 84, 108, 378}, {2, 3, 7, 84, 112, 336}, {2, 3, 7,
   84, 120, 280}, {2, 3, 7, 84, 126, 252}, {2, 3, 7, 84, 132,
   231}, {2, 3, 7, 84, 133, 228}, {2, 3, 7, 84, 140, 210}, {2, 3, 7,
   84, 147, 196}, {2, 3, 7, 84, 156, 182}, {2, 3, 7, 85, 90,
   1071}, {2, 3, 7, 85, 140, 204}, {2, 3, 7, 87, 91, 754}, {2, 3, 7,
   88, 154, 168}, {2, 3, 7, 90, 91, 585}, {2, 3, 7, 90, 99, 385}, {2,
   3, 7, 90, 105, 315}, {2, 3, 7, 90, 126, 210}, {2, 3, 7, 90, 135,
   189}, {2, 3, 7, 90, 140, 180}, {2, 3, 7, 91, 96, 416}, {2, 3, 7,
   91, 104, 312}, {2, 3, 7, 91, 114, 247}, {2, 3, 7, 91, 117,
   234}, {2, 3, 7, 91, 130, 195}, {2, 3, 7, 95, 105, 266}, {2, 3, 7,
   96, 112, 224}, {2, 3, 7, 96, 140, 160}, {2, 3, 7, 98, 105,
   245}, {2, 3, 7, 100, 140, 150}, {2, 3, 7, 105, 119, 170}, {2, 3, 7,
    105, 120, 168}, {2, 3, 7, 108, 135, 140}, {2, 3, 7, 110, 132,
   140}, {2, 3, 7, 112, 126, 144}, {2, 3, 8, 25, 601, 360600}, {2, 3,
   8, 25, 602, 180600}, {2, 3, 8, 25, 603, 120600}, {2, 3, 8, 25, 604,
    90600}, {2, 3, 8, 25, 605, 72600}, {2, 3, 8, 25, 606, 60600}, {2,
   3, 8, 25, 608, 45600}, {2, 3, 8, 25, 609, 40600}, {2, 3, 8, 25,
   610, 36600}, {2, 3, 8, 25, 612, 30600}, {2, 3, 8, 25, 615,
   24600}, {2, 3, 8, 25, 616, 23100}, {2, 3, 8, 25, 618, 20600}, {2,
   3, 8, 25, 620, 18600}, {2, 3, 8, 25, 624, 15600}, {2, 3, 8, 25,
   625, 15000}, {2, 3, 8, 25, 630, 12600}, {2, 3, 8, 25, 632,
   11850}, {2, 3, 8, 25, 636, 10600}, {2, 3, 8, 25, 640, 9600}, {2, 3,
    8, 25, 645, 8600}, {2, 3, 8, 25, 648, 8100}, {2, 3, 8, 25, 650,
   7800}, {2, 3, 8, 25, 660, 6600}, {2, 3, 8, 25, 664, 6225}, {2, 3,
   8, 25, 672, 5600}, {2, 3, 8, 25, 675, 5400}, {2, 3, 8, 25, 680,
   5100}, {2, 3, 8, 25, 690, 4600}, {2, 3, 8, 25, 696, 4350}, {2, 3,
   8, 25, 700, 4200}, {2, 3, 8, 25, 720, 3600}, {2, 3, 8, 25, 725,
   3480}, {2, 3, 8, 25, 744, 3100}, {2, 3, 8, 25, 750, 3000}, {2, 3,
   8, 25, 760, 2850}, {2, 3, 8, 25, 780, 2600}, {2, 3, 8, 25, 792,
   2475}, {2, 3, 8, 25, 800, 2400}, {2, 3, 8, 25, 825, 2200}, {2, 3,
   8, 25, 840, 2100}, {2, 3, 8, 25, 850, 2040}, {2, 3, 8, 25, 888,
   1850}, {2, 3, 8, 25, 900, 1800}, {2, 3, 8, 25, 920, 1725}, {2, 3,
   8, 25, 960, 1600}, {2, 3, 8, 25, 975, 1560}, {2, 3, 8, 25, 1000,
   1500}, {2, 3, 8, 25, 1050, 1400}, {2, 3, 8, 25, 1080, 1350}, {2, 3,
    8, 25, 1100, 1320}, {2, 3, 8, 25, 1176, 1225}, {2, 3, 8, 26, 313,
   97656}, {2, 3, 8, 26, 314, 48984}, {2, 3, 8, 26, 315, 32760}, {2,
   3, 8, 26, 316, 24648}, {2, 3, 8, 26, 318, 16536}, {2, 3, 8, 26,
   320, 12480}, {2, 3, 8, 26, 321, 11128}, {2, 3, 8, 26, 324,
   8424}, {2, 3, 8, 26, 325, 7800}, {2, 3, 8, 26, 328, 6396}, {2, 3,
   8, 26, 330, 5720}, {2, 3, 8, 26, 336, 4368}, {2, 3, 8, 26, 338,
   4056}, {2, 3, 8, 26, 344, 3354}, {2, 3, 8, 26, 348, 3016}, {2, 3,
   8, 26, 351, 2808}, {2, 3, 8, 26, 360, 2340}, {2, 3, 8, 26, 364,
   2184}, {2, 3, 8, 26, 376, 1833}, {2, 3, 8, 26, 384, 1664}, {2, 3,
   8, 26, 390, 1560}, {2, 3, 8, 26, 408, 1326}, {2, 3, 8, 26, 416,
   1248}, {2, 3, 8, 26, 429, 1144}, {2, 3, 8, 26, 456, 988}, {2, 3, 8,
    26, 468, 936}, {2, 3, 8, 26, 481, 888}, {2, 3, 8, 26, 504,
   819}, {2, 3, 8, 26, 520, 780}, {2, 3, 8, 26, 546, 728}, {2, 3, 8,
   26, 600, 650}, {2, 3, 8, 27, 217, 46872}, {2, 3, 8, 27, 218,
   23544}, {2, 3, 8, 27, 219, 15768}, {2, 3, 8, 27, 220, 11880}, {2,
   3, 8, 27, 222, 7992}, {2, 3, 8, 27, 224, 6048}, {2, 3, 8, 27, 225,
   5400}, {2, 3, 8, 27, 228, 4104}, {2, 3, 8, 27, 232, 3132}, {2, 3,
   8, 27, 234, 2808}, {2, 3, 8, 27, 240, 2160}, {2, 3, 8, 27, 243,
   1944}, {2, 3, 8, 27, 248, 1674}, {2, 3, 8, 27, 252, 1512}, {2, 3,
   8, 27, 264, 1188}, {2, 3, 8, 27, 270, 1080}, {2, 3, 8, 27, 280,
   945}, {2, 3, 8, 27, 288, 864}, {2, 3, 8, 27, 297, 792}, {2, 3, 8,
   27, 312, 702}, {2, 3, 8, 27, 324, 648}, {2, 3, 8, 27, 360,
   540}, {2, 3, 8, 27, 378, 504}, {2, 3, 8, 27, 408, 459}, {2, 3, 8,
   28, 169, 28392}, {2, 3, 8, 28, 170, 14280}, {2, 3, 8, 28, 171,
   9576}, {2, 3, 8, 28, 172, 7224}, {2, 3, 8, 28, 174, 4872}, {2, 3,
   8, 28, 175, 4200}, {2, 3, 8, 28, 176, 3696}, {2, 3, 8, 28, 177,
   3304}, {2, 3, 8, 28, 180, 2520}, {2, 3, 8, 28, 182, 2184}, {2, 3,
   8, 28, 184, 1932}, {2, 3, 8, 28, 186, 1736}, {2, 3, 8, 28, 189,
   1512}, {2, 3, 8, 28, 192, 1344}, {2, 3, 8, 28, 196, 1176}, {2, 3,
   8, 28, 200, 1050}, {2, 3, 8, 28, 204, 952}, {2, 3, 8, 28, 210,
   840}, {2, 3, 8, 28, 216, 756}, {2, 3, 8, 28, 217, 744}, {2, 3, 8,
   28, 224, 672}, {2, 3, 8, 28, 231, 616}, {2, 3, 8, 28, 232,
   609}, {2, 3, 8, 28, 240, 560}, {2, 3, 8, 28, 252, 504}, {2, 3, 8,
   28, 264, 462}, {2, 3, 8, 28, 266, 456}, {2, 3, 8, 28, 280,
   420}, {2, 3, 8, 28, 294, 392}, {2, 3, 8, 28, 312, 364}, {2, 3, 8,
   28, 315, 360}, {2, 3, 8, 29, 140, 24360}, {2, 3, 8, 29, 141,
   10904}, {2, 3, 8, 29, 144, 4176}, {2, 3, 8, 29, 145, 3480}, {2, 3,
   8, 29, 152, 1653}, {2, 3, 8, 29, 168, 812}, {2, 3, 8, 29, 174,
   696}, {2, 3, 8, 29, 232, 348}, {2, 3, 8, 30, 121, 14520}, {2, 3, 8,
    30, 122, 7320}, {2, 3, 8, 30, 123, 4920}, {2, 3, 8, 30, 124,
   3720}, {2, 3, 8, 30, 125, 3000}, {2, 3, 8, 30, 126, 2520}, {2, 3,
   8, 30, 128, 1920}, {2, 3, 8, 30, 129, 1720}, {2, 3, 8, 30, 130,
   1560}, {2, 3, 8, 30, 132, 1320}, {2, 3, 8, 30, 135, 1080}, {2, 3,
   8, 30, 136, 1020}, {2, 3, 8, 30, 138, 920}, {2, 3, 8, 30, 140,
   840}, {2, 3, 8, 30, 144, 720}, {2, 3, 8, 30, 145, 696}, {2, 3, 8,
   30, 150, 600}, {2, 3, 8, 30, 152, 570}, {2, 3, 8, 30, 156,
   520}, {2, 3, 8, 30, 160, 480}, {2, 3, 8, 30, 165, 440}, {2, 3, 8,
   30, 168, 420}, {2, 3, 8, 30, 170, 408}, {2, 3, 8, 30, 180,
   360}, {2, 3, 8, 30, 184, 345}, {2, 3, 8, 30, 192, 320}, {2, 3, 8,
   30, 195, 312}, {2, 3, 8, 30, 200, 300}, {2, 3, 8, 30, 210,
   280}, {2, 3, 8, 30, 216, 270}, {2, 3, 8, 30, 220, 264}, {2, 3, 8,
   31, 108, 6696}, {2, 3, 8, 31, 120, 930}, {2, 3, 8, 31, 124,
   744}, {2, 3, 8, 31, 186, 248}, {2, 3, 8, 32, 97, 9312}, {2, 3, 8,
   32, 98, 4704}, {2, 3, 8, 32, 99, 3168}, {2, 3, 8, 32, 100,
   2400}, {2, 3, 8, 32, 102, 1632}, {2, 3, 8, 32, 104, 1248}, {2, 3,
   8, 32, 105, 1120}, {2, 3, 8, 32, 108, 864}, {2, 3, 8, 32, 112,
   672}, {2, 3, 8, 32, 114, 608}, {2, 3, 8, 32, 120, 480}, {2, 3, 8,
   32, 128, 384}, {2, 3, 8, 32, 132, 352}, {2, 3, 8, 32, 144,
   288}, {2, 3, 8, 32, 160, 240}, {2, 3, 8, 32, 168, 224}, {2, 3, 8,
   33, 89, 7832}, {2, 3, 8, 33, 90, 3960}, {2, 3, 8, 33, 92,
   2024}, {2, 3, 8, 33, 96, 1056}, {2, 3, 8, 33, 99, 792}, {2, 3, 8,
   33, 104, 572}, {2, 3, 8, 33, 110, 440}, {2, 3, 8, 33, 120,
   330}, {2, 3, 8, 33, 132, 264}, {2, 3, 8, 33, 152, 209}, {2, 3, 8,
   34, 82, 16728}, {2, 3, 8, 34, 84, 2856}, {2, 3, 8, 34, 85,
   2040}, {2, 3, 8, 34, 88, 1122}, {2, 3, 8, 34, 96, 544}, {2, 3, 8,
   34, 102, 408}, {2, 3, 8, 34, 120, 255}, {2, 3, 8, 34, 136,
   204}, {2, 3, 8, 35, 77, 9240}, {2, 3, 8, 35, 78, 3640}, {2, 3, 8,
   35, 80, 1680}, {2, 3, 8, 35, 84, 840}, {2, 3, 8, 35, 90, 504}, {2,
   3, 8, 35, 105, 280}, {2, 3, 8, 35, 112, 240}, {2, 3, 8, 35, 120,
   210}, {2, 3, 8, 35, 140, 168}, {2, 3, 8, 36, 73, 5256}, {2, 3, 8,
   36, 74, 2664}, {2, 3, 8, 36, 75, 1800}, {2, 3, 8, 36, 76,
   1368}, {2, 3, 8, 36, 78, 936}, {2, 3, 8, 36, 80, 720}, {2, 3, 8,
   36, 81, 648}, {2, 3, 8, 36, 84, 504}, {2, 3, 8, 36, 88, 396}, {2,
   3, 8, 36, 90, 360}, {2, 3, 8, 36, 96, 288}, {2, 3, 8, 36, 99,
   264}, {2, 3, 8, 36, 104, 234}, {2, 3, 8, 36, 108, 216}, {2, 3, 8,
   36, 120, 180}, {2, 3, 8, 36, 126, 168}, {2, 3, 8, 36, 136,
   153}, {2, 3, 8, 37, 69, 6808}, {2, 3, 8, 37, 72, 1332}, {2, 3, 8,
   37, 74, 888}, {2, 3, 8, 38, 66, 5016}, {2, 3, 8, 38, 72, 684}, {2,
   3, 8, 38, 76, 456}, {2, 3, 8, 38, 114, 152}, {2, 3, 8, 39, 63,
   6552}, {2, 3, 8, 39, 64, 2496}, {2, 3, 8, 39, 65, 1560}, {2, 3, 8,
   39, 66, 1144}, {2, 3, 8, 39, 72, 468}, {2, 3, 8, 39, 78, 312}, {2,
   3, 8, 39, 104, 156}, {2, 3, 8, 39, 120, 130}, {2, 3, 8, 40, 61,
   3660}, {2, 3, 8, 40, 62, 1860}, {2, 3, 8, 40, 63, 1260}, {2, 3, 8,
   40, 64, 960}, {2, 3, 8, 40, 65, 780}, {2, 3, 8, 40, 66, 660}, {2,
   3, 8, 40, 68, 510}, {2, 3, 8, 40, 69, 460}, {2, 3, 8, 40, 70,
   420}, {2, 3, 8, 40, 72, 360}, {2, 3, 8, 40, 75, 300}, {2, 3, 8, 40,
    76, 285}, {2, 3, 8, 40, 78, 260}, {2, 3, 8, 40, 80, 240}, {2, 3,
   8, 40, 84, 210}, {2, 3, 8, 40, 85, 204}, {2, 3, 8, 40, 90,
   180}, {2, 3, 8, 40, 96, 160}, {2, 3, 8, 40, 100, 150}, {2, 3, 8,
   40, 105, 140}, {2, 3, 8, 40, 108, 135}, {2, 3, 8, 40, 110,
   132}, {2, 3, 8, 41, 58, 28536}, {2, 3, 8, 41, 60, 1640}, {2, 3, 8,
   42, 57, 3192}, {2, 3, 8, 42, 58, 1624}, {2, 3, 8, 42, 60, 840}, {2,
    3, 8, 42, 63, 504}, {2, 3, 8, 42, 64, 448}, {2, 3, 8, 42, 70,
   280}, {2, 3, 8, 42, 72, 252}, {2, 3, 8, 42, 84, 168}, {2, 3, 8, 42,
    88, 154}, {2, 3, 8, 42, 105, 120}, {2, 3, 8, 43, 56, 1806}, {2, 3,
    8, 44, 53, 13992}, {2, 3, 8, 44, 54, 2376}, {2, 3, 8, 44, 55,
   1320}, {2, 3, 8, 44, 56, 924}, {2, 3, 8, 44, 60, 440}, {2, 3, 8,
   44, 66, 264}, {2, 3, 8, 44, 72, 198}, {2, 3, 8, 44, 77, 168}, {2,
   3, 8, 44, 88, 132}, {2, 3, 8, 45, 52, 4680}, {2, 3, 8, 45, 54,
   1080}, {2, 3, 8, 45, 55, 792}, {2, 3, 8, 45, 56, 630}, {2, 3, 8,
   45, 60, 360}, {2, 3, 8, 45, 63, 280}, {2, 3, 8, 45, 72, 180}, {2,
   3, 8, 45, 80, 144}, {2, 3, 8, 45, 90, 120}, {2, 3, 8, 46, 51,
   3128}, {2, 3, 8, 46, 56, 483}, {2, 3, 8, 46, 69, 184}, {2, 3, 8,
   48, 49, 2352}, {2, 3, 8, 48, 50, 1200}, {2, 3, 8, 48, 51, 816}, {2,
    3, 8, 48, 52, 624}, {2, 3, 8, 48, 54, 432}, {2, 3, 8, 48, 56,
   336}, {2, 3, 8, 48, 57, 304}, {2, 3, 8, 48, 60, 240}, {2, 3, 8, 48,
    64, 192}, {2, 3, 8, 48, 66, 176}, {2, 3, 8, 48, 72, 144}, {2, 3,
   8, 48, 80, 120}, {2, 3, 8, 48, 84, 112}, {2, 3, 8, 49, 56,
   294}, {2, 3, 8, 50, 60, 200}, {2, 3, 8, 50, 75, 120}, {2, 3, 8, 51,
    56, 238}, {2, 3, 8, 51, 68, 136}, {2, 3, 8, 52, 72, 117}, {2, 3,
   8, 52, 78, 104}, {2, 3, 8, 54, 56, 189}, {2, 3, 8, 54, 72,
   108}, {2, 3, 8, 55, 66, 120}, {2, 3, 8, 56, 60, 140}, {2, 3, 8, 56,
    63, 126}, {2, 3, 8, 56, 70, 105}, {2, 3, 8, 56, 78, 91}, {2, 3, 8,
    60, 65, 104}, {2, 3, 8, 60, 72, 90}, {2, 3, 8, 63, 72, 84}, {2, 3,
    9, 19, 343, 117306}, {2, 3, 9, 19, 344, 58824}, {2, 3, 9, 19, 345,
    39330}, {2, 3, 9, 19, 346, 29583}, {2, 3, 9, 19, 348, 19836}, {2,
   3, 9, 19, 351, 13338}, {2, 3, 9, 19, 354, 10089}, {2, 3, 9, 19,
   360, 6840}, {2, 3, 9, 19, 361, 6498}, {2, 3, 9, 19, 369, 4674}, {2,
    3, 9, 19, 378, 3591}, {2, 3, 9, 19, 380, 3420}, {2, 3, 9, 19, 396,
    2508}, {2, 3, 9, 19, 399, 2394}, {2, 3, 9, 19, 418, 1881}, {2, 3,
   9, 19, 423, 1786}, {2, 3, 9, 19, 450, 1425}, {2, 3, 9, 19, 456,
   1368}, {2, 3, 9, 19, 504, 1064}, {2, 3, 9, 19, 513, 1026}, {2, 3,
   9, 19, 570, 855}, {2, 3, 9, 19, 666, 703}, {2, 3, 9, 20, 181,
   32580}, {2, 3, 9, 20, 182, 16380}, {2, 3, 9, 20, 183, 10980}, {2,
   3, 9, 20, 184, 8280}, {2, 3, 9, 20, 185, 6660}, {2, 3, 9, 20, 186,
   5580}, {2, 3, 9, 20, 188, 4230}, {2, 3, 9, 20, 189, 3780}, {2, 3,
   9, 20, 190, 3420}, {2, 3, 9, 20, 192, 2880}, {2, 3, 9, 20, 195,
   2340}, {2, 3, 9, 20, 196, 2205}, {2, 3, 9, 20, 198, 1980}, {2, 3,
   9, 20, 200, 1800}, {2, 3, 9, 20, 204, 1530}, {2, 3, 9, 20, 205,
   1476}, {2, 3, 9, 20, 207, 1380}, {2, 3, 9, 20, 210, 1260}, {2, 3,
   9, 20, 216, 1080}, {2, 3, 9, 20, 220, 990}, {2, 3, 9, 20, 225,
   900}, {2, 3, 9, 20, 228, 855}, {2, 3, 9, 20, 230, 828}, {2, 3, 9,
   20, 234, 780}, {2, 3, 9, 20, 240, 720}, {2, 3, 9, 20, 252,
   630}, {2, 3, 9, 20, 255, 612}, {2, 3, 9, 20, 260, 585}, {2, 3, 9,
   20, 261, 580}, {2, 3, 9, 20, 270, 540}, {2, 3, 9, 20, 280,
   504}, {2, 3, 9, 20, 288, 480}, {2, 3, 9, 20, 300, 450}, {2, 3, 9,
   20, 315, 420}, {2, 3, 9, 20, 324, 405}, {2, 3, 9, 20, 330,
   396}, {2, 3, 9, 20, 342, 380}, {2, 3, 9, 21, 127, 16002}, {2, 3, 9,
    21, 128, 8064}, {2, 3, 9, 21, 129, 5418}, {2, 3, 9, 21, 130,
   4095}, {2, 3, 9, 21, 132, 2772}, {2, 3, 9, 21, 133, 2394}, {2, 3,
   9, 21, 135, 1890}, {2, 3, 9, 21, 138, 1449}, {2, 3, 9, 21, 140,
   1260}, {2, 3, 9, 21, 144, 1008}, {2, 3, 9, 21, 147, 882}, {2, 3, 9,
    21, 153, 714}, {2, 3, 9, 21, 154, 693}, {2, 3, 9, 21, 162,
   567}, {2, 3, 9, 21, 168, 504}, {2, 3, 9, 21, 175, 450}, {2, 3, 9,
   21, 180, 420}, {2, 3, 9, 21, 189, 378}, {2, 3, 9, 21, 207,
   322}, {2, 3, 9, 21, 210, 315}, {2, 3, 9, 21, 224, 288}, {2, 3, 9,
   21, 234, 273}, {2, 3, 9, 22, 100, 9900}, {2, 3, 9, 22, 102,
   3366}, {2, 3, 9, 22, 108, 1188}, {2, 3, 9, 22, 110, 990}, {2, 3, 9,
    22, 126, 462}, {2, 3, 9, 22, 132, 396}, {2, 3, 9, 22, 180,
   220}, {2, 3, 9, 23, 83, 34362}, {2, 3, 9, 23, 84, 5796}, {2, 3, 9,
   23, 90, 1035}, {2, 3, 9, 23, 92, 828}, {2, 3, 9, 23, 99, 506}, {2,
   3, 9, 23, 138, 207}, {2, 3, 9, 24, 73, 5256}, {2, 3, 9, 24, 74,
   2664}, {2, 3, 9, 24, 75, 1800}, {2, 3, 9, 24, 76, 1368}, {2, 3, 9,
   24, 78, 936}, {2, 3, 9, 24, 80, 720}, {2, 3, 9, 24, 81, 648}, {2,
   3, 9, 24, 84, 504}, {2, 3, 9, 24, 88, 396}, {2, 3, 9, 24, 90,
   360}, {2, 3, 9, 24, 96, 288}, {2, 3, 9, 24, 99, 264}, {2, 3, 9, 24,
    104, 234}, {2, 3, 9, 24, 108, 216}, {2, 3, 9, 24, 120, 180}, {2,
   3, 9, 24, 126, 168}, {2, 3, 9, 24, 136, 153}, {2, 3, 9, 25, 65,
   5850}, {2, 3, 9, 25, 66, 2475}, {2, 3, 9, 25, 72, 600}, {2, 3, 9,
   25, 75, 450}, {2, 3, 9, 25, 90, 225}, {2, 3, 9, 25, 100, 180}, {2,
   3, 9, 26, 59, 6903}, {2, 3, 9, 26, 60, 2340}, {2, 3, 9, 26, 63,
   819}, {2, 3, 9, 26, 65, 585}, {2, 3, 9, 26, 72, 312}, {2, 3, 9, 26,
    78, 234}, {2, 3, 9, 26, 99, 143}, {2, 3, 9, 27, 55, 2970}, {2, 3,
   9, 27, 56, 1512}, {2, 3, 9, 27, 57, 1026}, {2, 3, 9, 27, 58,
   783}, {2, 3, 9, 27, 60, 540}, {2, 3, 9, 27, 63, 378}, {2, 3, 9, 27,
    66, 297}, {2, 3, 9, 27, 72, 216}, {2, 3, 9, 27, 81, 162}, {2, 3,
   9, 27, 90, 135}, {2, 3, 9, 28, 51, 4284}, {2, 3, 9, 28, 52,
   1638}, {2, 3, 9, 28, 54, 756}, {2, 3, 9, 28, 56, 504}, {2, 3, 9,
   28, 60, 315}, {2, 3, 9, 28, 63, 252}, {2, 3, 9, 28, 70, 180}, {2,
   3, 9, 28, 72, 168}, {2, 3, 9, 28, 84, 126}, {2, 3, 9, 29, 48,
   4176}, {2, 3, 9, 29, 58, 261}, {2, 3, 9, 30, 46, 2070}, {2, 3, 9,
   30, 48, 720}, {2, 3, 9, 30, 50, 450}, {2, 3, 9, 30, 54, 270}, {2,
   3, 9, 30, 60, 180}, {2, 3, 9, 30, 70, 126}, {2, 3, 9, 30, 72,
   120}, {2, 3, 9, 31, 43, 23994}, {2, 3, 9, 31, 45, 930}, {2, 3, 9,
   32, 42, 2016}, {2, 3, 9, 32, 45, 480}, {2, 3, 9, 32, 48, 288}, {2,
   3, 9, 32, 72, 96}, {2, 3, 9, 33, 40, 3960}, {2, 3, 9, 33, 42,
   693}, {2, 3, 9, 33, 44, 396}, {2, 3, 9, 33, 45, 330}, {2, 3, 9, 33,
    66, 99}, {2, 3, 9, 33, 72, 88}, {2, 3, 9, 34, 39, 1989}, {2, 3, 9,
    34, 45, 255}, {2, 3, 9, 34, 51, 153}, {2, 3, 9, 35, 40, 504}, {2,
   3, 9, 35, 42, 315}, {2, 3, 9, 35, 45, 210}, {2, 3, 9, 35, 63,
   90}, {2, 3, 9, 36, 37, 1332}, {2, 3, 9, 36, 38, 684}, {2, 3, 9, 36,
    39, 468}, {2, 3, 9, 36, 40, 360}, {2, 3, 9, 36, 42, 252}, {2, 3,
   9, 36, 44, 198}, {2, 3, 9, 36, 45, 180}, {2, 3, 9, 36, 48,
   144}, {2, 3, 9, 36, 52, 117}, {2, 3, 9, 36, 54, 108}, {2, 3, 9, 36,
    60, 90}, {2, 3, 9, 36, 63, 84}, {2, 3, 9, 39, 45, 130}, {2, 3, 9,
   40, 45, 120}, {2, 3, 9, 40, 60, 72}, {2, 3, 9, 42, 45, 105}, {2, 3,
    9, 42, 56, 72}, {2, 3, 9, 45, 48, 80}, {2, 3, 9, 45, 50, 75}, {2,
   3, 9, 45, 55, 66}, {2, 3, 10, 16, 241, 57840}, {2, 3, 10, 16, 242,
   29040}, {2, 3, 10, 16, 243, 19440}, {2, 3, 10, 16, 244, 14640}, {2,
    3, 10, 16, 245, 11760}, {2, 3, 10, 16, 246, 9840}, {2, 3, 10, 16,
   248, 7440}, {2, 3, 10, 16, 249, 6640}, {2, 3, 10, 16, 250,
   6000}, {2, 3, 10, 16, 252, 5040}, {2, 3, 10, 16, 255, 4080}, {2, 3,
    10, 16, 256, 3840}, {2, 3, 10, 16, 258, 3440}, {2, 3, 10, 16, 260,
    3120}, {2, 3, 10, 16, 264, 2640}, {2, 3, 10, 16, 265, 2544}, {2,
   3, 10, 16, 270, 2160}, {2, 3, 10, 16, 272, 2040}, {2, 3, 10, 16,
   276, 1840}, {2, 3, 10, 16, 280, 1680}, {2, 3, 10, 16, 285,
   1520}, {2, 3, 10, 16, 288, 1440}, {2, 3, 10, 16, 290, 1392}, {2, 3,
    10, 16, 300, 1200}, {2, 3, 10, 16, 304, 1140}, {2, 3, 10, 16, 312,
    1040}, {2, 3, 10, 16, 315, 1008}, {2, 3, 10, 16, 320, 960}, {2, 3,
    10, 16, 330, 880}, {2, 3, 10, 16, 336, 840}, {2, 3, 10, 16, 340,
   816}, {2, 3, 10, 16, 360, 720}, {2, 3, 10, 16, 368, 690}, {2, 3,
   10, 16, 384, 640}, {2, 3, 10, 16, 390, 624}, {2, 3, 10, 16, 400,
   600}, {2, 3, 10, 16, 420, 560}, {2, 3, 10, 16, 432, 540}, {2, 3,
   10, 16, 440, 528}, {2, 3, 10, 16, 465, 496}, {2, 3, 10, 17, 128,
   32640}, {2, 3, 10, 17, 129, 10965}, {2, 3, 10, 17, 130, 6630}, {2,
   3, 10, 17, 132, 3740}, {2, 3, 10, 17, 135, 2295}, {2, 3, 10, 17,
   136, 2040}, {2, 3, 10, 17, 140, 1428}, {2, 3, 10, 17, 150,
   850}, {2, 3, 10, 17, 153, 765}, {2, 3, 10, 17, 165, 561}, {2, 3,
   10, 17, 170, 510}, {2, 3, 10, 17, 204, 340}, {2, 3, 10, 17, 240,
   272}, {2, 3, 10, 18, 91, 8190}, {2, 3, 10, 18, 92, 4140}, {2, 3,
   10, 18, 93, 2790}, {2, 3, 10, 18, 94, 2115}, {2, 3, 10, 18, 95,
   1710}, {2, 3, 10, 18, 96, 1440}, {2, 3, 10, 18, 99, 990}, {2, 3,
   10, 18, 100, 900}, {2, 3, 10, 18, 102, 765}, {2, 3, 10, 18, 105,
   630}, {2, 3, 10, 18, 108, 540}, {2, 3, 10, 18, 110, 495}, {2, 3,
   10, 18, 115, 414}, {2, 3, 10, 18, 117, 390}, {2, 3, 10, 18, 120,
   360}, {2, 3, 10, 18, 126, 315}, {2, 3, 10, 18, 135, 270}, {2, 3,
   10, 18, 140, 252}, {2, 3, 10, 18, 144, 240}, {2, 3, 10, 18, 150,
   225}, {2, 3, 10, 18, 165, 198}, {2, 3, 10, 18, 171, 190}, {2, 3,
   10, 19, 72, 6840}, {2, 3, 10, 19, 75, 1425}, {2, 3, 10, 19, 76,
   1140}, {2, 3, 10, 19, 90, 342}, {2, 3, 10, 19, 95, 285}, {2, 3, 10,
    19, 114, 190}, {2, 3, 10, 20, 61, 3660}, {2, 3, 10, 20, 62,
   1860}, {2, 3, 10, 20, 63, 1260}, {2, 3, 10, 20, 64, 960}, {2, 3,
   10, 20, 65, 780}, {2, 3, 10, 20, 66, 660}, {2, 3, 10, 20, 68,
   510}, {2, 3, 10, 20, 69, 460}, {2, 3, 10, 20, 70, 420}, {2, 3, 10,
   20, 72, 360}, {2, 3, 10, 20, 75, 300}, {2, 3, 10, 20, 76, 285}, {2,
    3, 10, 20, 78, 260}, {2, 3, 10, 20, 80, 240}, {2, 3, 10, 20, 84,
   210}, {2, 3, 10, 20, 85, 204}, {2, 3, 10, 20, 90, 180}, {2, 3, 10,
   20, 96, 160}, {2, 3, 10, 20, 100, 150}, {2, 3, 10, 20, 105,
   140}, {2, 3, 10, 20, 108, 135}, {2, 3, 10, 20, 110, 132}, {2, 3,
   10, 21, 53, 5565}, {2, 3, 10, 21, 54, 1890}, {2, 3, 10, 21, 55,
   1155}, {2, 3, 10, 21, 56, 840}, {2, 3, 10, 21, 57, 665}, {2, 3, 10,
    21, 60, 420}, {2, 3, 10, 21, 63, 315}, {2, 3, 10, 21, 65,
   273}, {2, 3, 10, 21, 70, 210}, {2, 3, 10, 21, 75, 175}, {2, 3, 10,
   21, 77, 165}, {2, 3, 10, 21, 84, 140}, {2, 3, 10, 21, 90, 126}, {2,
    3, 10, 22, 48, 2640}, {2, 3, 10, 22, 50, 825}, {2, 3, 10, 22, 55,
   330}, {2, 3, 10, 22, 60, 220}, {2, 3, 10, 22, 66, 165}, {2, 3, 10,
   22, 90, 99}, {2, 3, 10, 23, 45, 1035}, {2, 3, 10, 23, 46, 690}, {2,
    3, 10, 23, 69, 115}, {2, 3, 10, 24, 41, 1640}, {2, 3, 10, 24, 42,
   840}, {2, 3, 10, 24, 44, 440}, {2, 3, 10, 24, 45, 360}, {2, 3, 10,
   24, 48, 240}, {2, 3, 10, 24, 50, 200}, {2, 3, 10, 24, 56, 140}, {2,
    3, 10, 24, 60, 120}, {2, 3, 10, 24, 65, 104}, {2, 3, 10, 24, 72,
   90}, {2, 3, 10, 25, 38, 2850}, {2, 3, 10, 25, 39, 975}, {2, 3, 10,
   25, 40, 600}, {2, 3, 10, 25, 42, 350}, {2, 3, 10, 25, 45, 225}, {2,
    3, 10, 25, 50, 150}, {2, 3, 10, 25, 60, 100}, {2, 3, 10, 26, 36,
   2340}, {2, 3, 10, 26, 39, 390}, {2, 3, 10, 26, 40, 312}, {2, 3, 10,
    26, 65, 78}, {2, 3, 10, 27, 34, 4590}, {2, 3, 10, 27, 35,
   945}, {2, 3, 10, 27, 36, 540}, {2, 3, 10, 27, 40, 216}, {2, 3, 10,
   27, 45, 135}, {2, 3, 10, 27, 54, 90}, {2, 3, 10, 28, 33, 1540}, {2,
    3, 10, 28, 35, 420}, {2, 3, 10, 28, 36, 315}, {2, 3, 10, 28, 40,
   168}, {2, 3, 10, 28, 42, 140}, {2, 3, 10, 28, 60, 70}, {2, 3, 10,
   30, 31, 930}, {2, 3, 10, 30, 32, 480}, {2, 3, 10, 30, 33, 330}, {2,
    3, 10, 30, 34, 255}, {2, 3, 10, 30, 35, 210}, {2, 3, 10, 30, 36,
   180}, {2, 3, 10, 30, 39, 130}, {2, 3, 10, 30, 40, 120}, {2, 3, 10,
   30, 42, 105}, {2, 3, 10, 30, 45, 90}, {2, 3, 10, 30, 48, 80}, {2,
   3, 10, 30, 50, 75}, {2, 3, 10, 30, 55, 66}, {2, 3, 10, 32, 40,
   96}, {2, 3, 10, 33, 40, 88}, {2, 3, 10, 35, 42, 70}, {2, 3, 10, 35,
    45, 63}, {2, 3, 10, 36, 40, 72}, {2, 3, 10, 36, 45, 60}, {2, 3,
   10, 40, 42, 56}, {2, 3, 11, 14, 232, 53592}, {2, 3, 11, 14, 234,
   18018}, {2, 3, 11, 14, 238, 7854}, {2, 3, 11, 14, 240, 6160}, {2,
   3, 11, 14, 242, 5082}, {2, 3, 11, 14, 252, 2772}, {2, 3, 11, 14,
   264, 1848}, {2, 3, 11, 14, 280, 1320}, {2, 3, 11, 14, 294,
   1078}, {2, 3, 11, 14, 308, 924}, {2, 3, 11, 14, 330, 770}, {2, 3,
   11, 14, 352, 672}, {2, 3, 11, 14, 378, 594}, {2, 3, 11, 15, 111,
   12210}, {2, 3, 11, 15, 112, 6160}, {2, 3, 11, 15, 114, 3135}, {2,
   3, 11, 15, 115, 2530}, {2, 3, 11, 15, 120, 1320}, {2, 3, 11, 15,
   121, 1210}, {2, 3, 11, 15, 130, 715}, {2, 3, 11, 15, 132, 660}, {2,
    3, 11, 15, 135, 594}, {2, 3, 11, 15, 154, 385}, {2, 3, 11, 15,
   160, 352}, {2, 3, 11, 15, 165, 330}, {2, 3, 11, 15, 210, 231}, {2,
   3, 11, 16, 76, 10032}, {2, 3, 11, 16, 77, 3696}, {2, 3, 11, 16, 78,
    2288}, {2, 3, 11, 16, 80, 1320}, {2, 3, 11, 16, 88, 528}, {2, 3,
   11, 16, 96, 352}, {2, 3, 11, 16, 110, 240}, {2, 3, 11, 16, 112,
   231}, {2, 3, 11, 16, 132, 176}, {2, 3, 11, 17, 60, 3740}, {2, 3,
   11, 17, 66, 561}, {2, 3, 11, 18, 50, 4950}, {2, 3, 11, 18, 51,
   1683}, {2, 3, 11, 18, 54, 594}, {2, 3, 11, 18, 55, 495}, {2, 3, 11,
    18, 63, 231}, {2, 3, 11, 18, 66, 198}, {2, 3, 11, 18, 90,
   110}, {2, 3, 11, 19, 44, 2508}, {2, 3, 11, 20, 39, 8580}, {2, 3,
   11, 20, 40, 1320}, {2, 3, 11, 20, 44, 330}, {2, 3, 11, 20, 55,
   132}, {2, 3, 11, 20, 60, 110}, {2, 3, 11, 21, 36, 2772}, {2, 3, 11,
    21, 42, 231}, {2, 3, 11, 21, 66, 77}, {2, 3, 11, 22, 34,
   1122}, {2, 3, 11, 22, 36, 396}, {2, 3, 11, 22, 42, 154}, {2, 3, 11,
    22, 44, 132}, {2, 3, 11, 23, 31, 47058}, {2, 3, 11, 23, 33,
   506}, {2, 3, 11, 24, 30, 1320}, {2, 3, 11, 24, 32, 352}, {2, 3, 11,
    24, 33, 264}, {2, 3, 11, 24, 40, 110}, {2, 3, 11, 24, 44, 88}, {2,
    3, 11, 25, 28, 23100}, {2, 3, 11, 26, 27, 3861}, {2, 3, 11, 26,
   33, 143}, {2, 3, 12, 13, 157, 24492}, {2, 3, 12, 13, 158,
   12324}, {2, 3, 12, 13, 159, 8268}, {2, 3, 12, 13, 160, 6240}, {2,
   3, 12, 13, 162, 4212}, {2, 3, 12, 13, 164, 3198}, {2, 3, 12, 13,
   165, 2860}, {2, 3, 12, 13, 168, 2184}, {2, 3, 12, 13, 169,
   2028}, {2, 3, 12, 13, 172, 1677}, {2, 3, 12, 13, 174, 1508}, {2, 3,
    12, 13, 180, 1170}, {2, 3, 12, 13, 182, 1092}, {2, 3, 12, 13, 192,
    832}, {2, 3, 12, 13, 195, 780}, {2, 3, 12, 13, 204, 663}, {2, 3,
   12, 13, 208, 624}, {2, 3, 12, 13, 228, 494}, {2, 3, 12, 13, 234,
   468}, {2, 3, 12, 13, 260, 390}, {2, 3, 12, 13, 273, 364}, {2, 3,
   12, 13, 300, 325}, {2, 3, 12, 14, 85, 7140}, {2, 3, 12, 14, 86,
   3612}, {2, 3, 12, 14, 87, 2436}, {2, 3, 12, 14, 88, 1848}, {2, 3,
   12, 14, 90, 1260}, {2, 3, 12, 14, 91, 1092}, {2, 3, 12, 14, 92,
   966}, {2, 3, 12, 14, 93, 868}, {2, 3, 12, 14, 96, 672}, {2, 3, 12,
   14, 98, 588}, {2, 3, 12, 14, 100, 525}, {2, 3, 12, 14, 102,
   476}, {2, 3, 12, 14, 105, 420}, {2, 3, 12, 14, 108, 378}, {2, 3,
   12, 14, 112, 336}, {2, 3, 12, 14, 120, 280}, {2, 3, 12, 14, 126,
   252}, {2, 3, 12, 14, 132, 231}, {2, 3, 12, 14, 133, 228}, {2, 3,
   12, 14, 140, 210}, {2, 3, 12, 14, 147, 196}, {2, 3, 12, 14, 156,
   182}, {2, 3, 12, 15, 61, 3660}, {2, 3, 12, 15, 62, 1860}, {2, 3,
   12, 15, 63, 1260}, {2, 3, 12, 15, 64, 960}, {2, 3, 12, 15, 65,
   780}, {2, 3, 12, 15, 66, 660}, {2, 3, 12, 15, 68, 510}, {2, 3, 12,
   15, 69, 460}, {2, 3, 12, 15, 70, 420}, {2, 3, 12, 15, 72, 360}, {2,
    3, 12, 15, 75, 300}, {2, 3, 12, 15, 76, 285}, {2, 3, 12, 15, 78,
   260}, {2, 3, 12, 15, 80, 240}, {2, 3, 12, 15, 84, 210}, {2, 3, 12,
   15, 85, 204}, {2, 3, 12, 15, 90, 180}, {2, 3, 12, 15, 96, 160}, {2,
    3, 12, 15, 100, 150}, {2, 3, 12, 15, 105, 140}, {2, 3, 12, 15,
   108, 135}, {2, 3, 12, 15, 110, 132}, {2, 3, 12, 16, 49, 2352}, {2,
   3, 12, 16, 50, 1200}, {2, 3, 12, 16, 51, 816}, {2, 3, 12, 16, 52,
   624}, {2, 3, 12, 16, 54, 432}, {2, 3, 12, 16, 56, 336}, {2, 3, 12,
   16, 57, 304}, {2, 3, 12, 16, 60, 240}, {2, 3, 12, 16, 64, 192}, {2,
    3, 12, 16, 66, 176}, {2, 3, 12, 16, 72, 144}, {2, 3, 12, 16, 80,
   120}, {2, 3, 12, 16, 84, 112}, {2, 3, 12, 17, 41, 8364}, {2, 3, 12,
    17, 42, 1428}, {2, 3, 12, 17, 44, 561}, {2, 3, 12, 17, 48,
   272}, {2, 3, 12, 17, 51, 204}, {2, 3, 12, 17, 68, 102}, {2, 3, 12,
   18, 37, 1332}, {2, 3, 12, 18, 38, 684}, {2, 3, 12, 18, 39,
   468}, {2, 3, 12, 18, 40, 360}, {2, 3, 12, 18, 42, 252}, {2, 3, 12,
   18, 44, 198}, {2, 3, 12, 18, 45, 180}, {2, 3, 12, 18, 48, 144}, {2,
    3, 12, 18, 52, 117}, {2, 3, 12, 18, 54, 108}, {2, 3, 12, 18, 60,
   90}, {2, 3, 12, 18, 63, 84}, {2, 3, 12, 19, 33, 2508}, {2, 3, 12,
   19, 36, 342}, {2, 3, 12, 19, 38, 228}, {2, 3, 12, 19, 57, 76}, {2,
   3, 12, 20, 31, 930}, {2, 3, 12, 20, 32, 480}, {2, 3, 12, 20, 33,
   330}, {2, 3, 12, 20, 34, 255}, {2, 3, 12, 20, 35, 210}, {2, 3, 12,
   20, 36, 180}, {2, 3, 12, 20, 39, 130}, {2, 3, 12, 20, 40, 120}, {2,
    3, 12, 20, 42, 105}, {2, 3, 12, 20, 45, 90}, {2, 3, 12, 20, 48,
   80}, {2, 3, 12, 20, 50, 75}, {2, 3, 12, 20, 55, 66}, {2, 3, 12, 21,
    29, 812}, {2, 3, 12, 21, 30, 420}, {2, 3, 12, 21, 32, 224}, {2, 3,
    12, 21, 35, 140}, {2, 3, 12, 21, 36, 126}, {2, 3, 12, 21, 42,
   84}, {2, 3, 12, 21, 44, 77}, {2, 3, 12, 22, 27, 1188}, {2, 3, 12,
   22, 28, 462}, {2, 3, 12, 22, 30, 220}, {2, 3, 12, 22, 33, 132}, {2,
    3, 12, 22, 36, 99}, {2, 3, 12, 22, 44, 66}, {2, 3, 12, 24, 25,
   600}, {2, 3, 12, 24, 26, 312}, {2, 3, 12, 24, 27, 216}, {2, 3, 12,
   24, 28, 168}, {2, 3, 12, 24, 30, 120}, {2, 3, 12, 24, 32, 96}, {2,
   3, 12, 24, 33, 88}, {2, 3, 12, 24, 36, 72}, {2, 3, 12, 24, 40,
   60}, {2, 3, 12, 24, 42, 56}, {2, 3, 12, 25, 30, 100}, {2, 3, 12,
   26, 39, 52}, {2, 3, 12, 27, 36, 54}, {2, 3, 12, 28, 30, 70}, {2, 3,
    12, 30, 36, 45}, {2, 3, 13, 14, 56, 2184}, {2, 3, 13, 14, 78,
   182}, {2, 3, 13, 14, 84, 156}, {2, 3, 13, 15, 44, 2860}, {2, 3, 13,
    15, 45, 1170}, {2, 3, 13, 15, 50, 325}, {2, 3, 13, 15, 52,
   260}, {2, 3, 13, 15, 60, 156}, {2, 3, 13, 15, 65, 130}, {2, 3, 13,
   16, 39, 624}, {2, 3, 13, 16, 48, 156}, {2, 3, 13, 17, 34, 663}, {2,
    3, 13, 18, 30, 1170}, {2, 3, 13, 18, 36, 156}, {2, 3, 13, 18, 39,
   117}, {2, 3, 13, 19, 27, 13338}, {2, 3, 13, 20, 26, 780}, {2, 3,
   13, 20, 30, 156}, {2, 3, 13, 21, 24, 2184}, {2, 3, 13, 21, 26,
   273}, {2, 3, 13, 21, 28, 156}, {2, 3, 13, 24, 26, 104}, {2, 3, 14,
   15, 36, 1260}, {2, 3, 14, 15, 40, 280}, {2, 3, 14, 15, 42,
   210}, {2, 3, 14, 15, 60, 84}, {2, 3, 14, 16, 32, 672}, {2, 3, 14,
   16, 35, 240}, {2, 3, 14, 16, 42, 112}, {2, 3, 14, 16, 48, 84}, {2,
   3, 14, 17, 28, 1428}, {2, 3, 14, 18, 26, 819}, {2, 3, 14, 18, 27,
   378}, {2, 3, 14, 18, 28, 252}, {2, 3, 14, 18, 35, 90}, {2, 3, 14,
   18, 36, 84}, {2, 3, 14, 18, 42, 63}, {2, 3, 14, 19, 24, 1064}, {2,
   3, 14, 20, 24, 280}, {2, 3, 14, 20, 28, 105}, {2, 3, 14, 20, 30,
   84}, {2, 3, 14, 20, 35, 60}, {2, 3, 14, 21, 22, 462}, {2, 3, 14,
   21, 24, 168}, {2, 3, 14, 21, 28, 84}, {2, 3, 14, 21, 30, 70}, {2,
   3, 14, 24, 28, 56}, {2, 3, 14, 24, 35, 40}, {2, 3, 15, 16, 27,
   2160}, {2, 3, 15, 16, 28, 560}, {2, 3, 15, 16, 30, 240}, {2, 3, 15,
    16, 32, 160}, {2, 3, 15, 16, 35, 112}, {2, 3, 15, 16, 40, 80}, {2,
    3, 15, 16, 48, 60}, {2, 3, 15, 17, 25, 850}, {2, 3, 15, 17, 34,
   85}, {2, 3, 15, 18, 23, 1035}, {2, 3, 15, 18, 24, 360}, {2, 3, 15,
   18, 25, 225}, {2, 3, 15, 18, 27, 135}, {2, 3, 15, 18, 30, 90}, {2,
   3, 15, 18, 35, 63}, {2, 3, 15, 18, 36, 60}, {2, 3, 15, 20, 21,
   420}, {2, 3, 15, 20, 22, 220}, {2, 3, 15, 20, 24, 120}, {2, 3, 15,
   20, 25, 100}, {2, 3, 15, 20, 28, 70}, {2, 3, 15, 20, 30, 60}, {2,
   3, 15, 20, 36, 45}, {2, 3, 15, 21, 28, 60}, {2, 3, 15, 21, 35,
   42}, {2, 3, 15, 24, 30, 40}, {2, 3, 16, 17, 24, 272}, {2, 3, 16,
   18, 21, 1008}, {2, 3, 16, 18, 24, 144}, {2, 3, 16, 18, 36, 48}, {2,
    3, 16, 20, 24, 80}, {2, 3, 16, 20, 30, 48}, {2, 3, 16, 21, 28,
   48}, {2, 3, 18, 20, 30, 36}, {2, 3, 18, 21, 28, 36}, {2, 3, 20, 21,
    28, 30}}

1591个解。

{{2, 4, 5, 21, 421, 176820}, {2, 4, 5, 21, 422, 88620}, {2, 4, 5, 21,
   423, 59220}, {2, 4, 5, 21, 424, 44520}, {2, 4, 5, 21, 425,
   35700}, {2, 4, 5, 21, 426, 29820}, {2, 4, 5, 21, 427, 25620}, {2,
   4, 5, 21, 428, 22470}, {2, 4, 5, 21, 429, 20020}, {2, 4, 5, 21,
   430, 18060}, {2, 4, 5, 21, 432, 15120}, {2, 4, 5, 21, 434,
   13020}, {2, 4, 5, 21, 435, 12180}, {2, 4, 5, 21, 436, 11445}, {2,
   4, 5, 21, 438, 10220}, {2, 4, 5, 21, 440, 9240}, {2, 4, 5, 21, 441,
    8820}, {2, 4, 5, 21, 444, 7770}, {2, 4, 5, 21, 445, 7476}, {2, 4,
   5, 21, 448, 6720}, {2, 4, 5, 21, 450, 6300}, {2, 4, 5, 21, 455,
   5460}, {2, 4, 5, 21, 456, 5320}, {2, 4, 5, 21, 460, 4830}, {2, 4,
   5, 21, 462, 4620}, {2, 4, 5, 21, 465, 4340}, {2, 4, 5, 21, 468,
   4095}, {2, 4, 5, 21, 469, 4020}, {2, 4, 5, 21, 470, 3948}, {2, 4,
   5, 21, 476, 3570}, {2, 4, 5, 21, 480, 3360}, {2, 4, 5, 21, 483,
   3220}, {2, 4, 5, 21, 490, 2940}, {2, 4, 5, 21, 492, 2870}, {2, 4,
   5, 21, 495, 2772}, {2, 4, 5, 21, 500, 2625}, {2, 4, 5, 21, 504,
   2520}, {2, 4, 5, 21, 510, 2380}, {2, 4, 5, 21, 518, 2220}, {2, 4,
   5, 21, 520, 2184}, {2, 4, 5, 21, 525, 2100}, {2, 4, 5, 21, 532,
   1995}, {2, 4, 5, 21, 540, 1890}, {2, 4, 5, 21, 546, 1820}, {2, 4,
   5, 21, 560, 1680}, {2, 4, 5, 21, 564, 1645}, {2, 4, 5, 21, 567,
   1620}, {2, 4, 5, 21, 570, 1596}, {2, 4, 5, 21, 588, 1470}, {2, 4,
   5, 21, 595, 1428}, {2, 4, 5, 21, 600, 1400}, {2, 4, 5, 21, 616,
   1320}, {2, 4, 5, 21, 620, 1302}, {2, 4, 5, 21, 630, 1260}, {2, 4,
   5, 21, 645, 1204}, {2, 4, 5, 21, 660, 1155}, {2, 4, 5, 21, 665,
   1140}, {2, 4, 5, 21, 672, 1120}, {2, 4, 5, 21, 700, 1050}, {2, 4,
   5, 21, 714, 1020}, {2, 4, 5, 21, 720, 1008}, {2, 4, 5, 21, 735,
   980}, {2, 4, 5, 21, 756, 945}, {2, 4, 5, 21, 770, 924}, {2, 4, 5,
   21, 780, 910}, {2, 4, 5, 21, 812, 870}, {2, 4, 5, 21, 820,
   861}, {2, 4, 5, 22, 221, 48620}, {2, 4, 5, 22, 222, 24420}, {2, 4,
   5, 22, 224, 12320}, {2, 4, 5, 22, 225, 9900}, {2, 4, 5, 22, 228,
   6270}, {2, 4, 5, 22, 230, 5060}, {2, 4, 5, 22, 231, 4620}, {2, 4,
   5, 22, 236, 3245}, {2, 4, 5, 22, 240, 2640}, {2, 4, 5, 22, 242,
   2420}, {2, 4, 5, 22, 245, 2156}, {2, 4, 5, 22, 260, 1430}, {2, 4,
   5, 22, 264, 1320}, {2, 4, 5, 22, 270, 1188}, {2, 4, 5, 22, 275,
   1100}, {2, 4, 5, 22, 300, 825}, {2, 4, 5, 22, 308, 770}, {2, 4, 5,
   22, 320, 704}, {2, 4, 5, 22, 330, 660}, {2, 4, 5, 22, 341,
   620}, {2, 4, 5, 22, 396, 495}, {2, 4, 5, 22, 420, 462}, {2, 4, 5,
   23, 154, 35420}, {2, 4, 5, 23, 155, 14260}, {2, 4, 5, 23, 156,
   8970}, {2, 4, 5, 23, 160, 3680}, {2, 4, 5, 23, 161, 3220}, {2, 4,
   5, 23, 170, 1564}, {2, 4, 5, 23, 180, 1035}, {2, 4, 5, 23, 184,
   920}, {2, 4, 5, 23, 220, 506}, {2, 4, 5, 23, 230, 460}, {2, 4, 5,
   23, 276, 345}, {2, 4, 5, 24, 121, 14520}, {2, 4, 5, 24, 122,
   7320}, {2, 4, 5, 24, 123, 4920}, {2, 4, 5, 24, 124, 3720}, {2, 4,
   5, 24, 125, 3000}, {2, 4, 5, 24, 126, 2520}, {2, 4, 5, 24, 128,
   1920}, {2, 4, 5, 24, 129, 1720}, {2, 4, 5, 24, 130, 1560}, {2, 4,
   5, 24, 132, 1320}, {2, 4, 5, 24, 135, 1080}, {2, 4, 5, 24, 136,
   1020}, {2, 4, 5, 24, 138, 920}, {2, 4, 5, 24, 140, 840}, {2, 4, 5,
   24, 144, 720}, {2, 4, 5, 24, 145, 696}, {2, 4, 5, 24, 150,
   600}, {2, 4, 5, 24, 152, 570}, {2, 4, 5, 24, 156, 520}, {2, 4, 5,
   24, 160, 480}, {2, 4, 5, 24, 165, 440}, {2, 4, 5, 24, 168,
   420}, {2, 4, 5, 24, 170, 408}, {2, 4, 5, 24, 180, 360}, {2, 4, 5,
   24, 184, 345}, {2, 4, 5, 24, 192, 320}, {2, 4, 5, 24, 195,
   312}, {2, 4, 5, 24, 200, 300}, {2, 4, 5, 24, 210, 280}, {2, 4, 5,
   24, 216, 270}, {2, 4, 5, 24, 220, 264}, {2, 4, 5, 25, 101,
   10100}, {2, 4, 5, 25, 102, 5100}, {2, 4, 5, 25, 104, 2600}, {2, 4,
   5, 25, 105, 2100}, {2, 4, 5, 25, 108, 1350}, {2, 4, 5, 25, 110,
   1100}, {2, 4, 5, 25, 116, 725}, {2, 4, 5, 25, 120, 600}, {2, 4, 5,
   25, 125, 500}, {2, 4, 5, 25, 140, 350}, {2, 4, 5, 25, 150,
   300}, {2, 4, 5, 25, 180, 225}, {2, 4, 5, 26, 87, 22620}, {2, 4, 5,
   26, 88, 5720}, {2, 4, 5, 26, 90, 2340}, {2, 4, 5, 26, 91,
   1820}, {2, 4, 5, 26, 92, 1495}, {2, 4, 5, 26, 95, 988}, {2, 4, 5,
   26, 100, 650}, {2, 4, 5, 26, 104, 520}, {2, 4, 5, 26, 120,
   312}, {2, 4, 5, 26, 130, 260}, {2, 4, 5, 26, 143, 220}, {2, 4, 5,
   26, 156, 195}, {2, 4, 5, 27, 78, 7020}, {2, 4, 5, 27, 80,
   2160}, {2, 4, 5, 27, 81, 1620}, {2, 4, 5, 27, 84, 945}, {2, 4, 5,
   27, 90, 540}, {2, 4, 5, 27, 108, 270}, {2, 4, 5, 27, 120, 216}, {2,
    4, 5, 27, 135, 180}, {2, 4, 5, 28, 71, 4970}, {2, 4, 5, 28, 72,
   2520}, {2, 4, 5, 28, 74, 1295}, {2, 4, 5, 28, 75, 1050}, {2, 4, 5,
   28, 77, 770}, {2, 4, 5, 28, 80, 560}, {2, 4, 5, 28, 84, 420}, {2,
   4, 5, 28, 90, 315}, {2, 4, 5, 28, 95, 266}, {2, 4, 5, 28, 98,
   245}, {2, 4, 5, 28, 105, 210}, {2, 4, 5, 28, 119, 170}, {2, 4, 5,
   28, 120, 168}, {2, 4, 5, 29, 65, 7540}, {2, 4, 5, 29, 70, 812}, {2,
    4, 5, 29, 116, 145}, {2, 4, 5, 30, 61, 3660}, {2, 4, 5, 30, 62,
   1860}, {2, 4, 5, 30, 63, 1260}, {2, 4, 5, 30, 64, 960}, {2, 4, 5,
   30, 65, 780}, {2, 4, 5, 30, 66, 660}, {2, 4, 5, 30, 68, 510}, {2,
   4, 5, 30, 69, 460}, {2, 4, 5, 30, 70, 420}, {2, 4, 5, 30, 72,
   360}, {2, 4, 5, 30, 75, 300}, {2, 4, 5, 30, 76, 285}, {2, 4, 5, 30,
    78, 260}, {2, 4, 5, 30, 80, 240}, {2, 4, 5, 30, 84, 210}, {2, 4,
   5, 30, 85, 204}, {2, 4, 5, 30, 90, 180}, {2, 4, 5, 30, 96,
   160}, {2, 4, 5, 30, 100, 150}, {2, 4, 5, 30, 105, 140}, {2, 4, 5,
   30, 108, 135}, {2, 4, 5, 30, 110, 132}, {2, 4, 5, 31, 60, 930}, {2,
    4, 5, 31, 62, 620}, {2, 4, 5, 32, 54, 4320}, {2, 4, 5, 32, 55,
   1760}, {2, 4, 5, 32, 56, 1120}, {2, 4, 5, 32, 60, 480}, {2, 4, 5,
   32, 64, 320}, {2, 4, 5, 32, 70, 224}, {2, 4, 5, 32, 80, 160}, {2,
   4, 5, 32, 96, 120}, {2, 4, 5, 33, 51, 11220}, {2, 4, 5, 33, 52,
   2145}, {2, 4, 5, 33, 55, 660}, {2, 4, 5, 33, 60, 330}, {2, 4, 5,
   33, 66, 220}, {2, 4, 5, 33, 88, 120}, {2, 4, 5, 34, 50, 1700}, {2,
   4, 5, 34, 51, 1020}, {2, 4, 5, 34, 60, 255}, {2, 4, 5, 34, 68,
   170}, {2, 4, 5, 35, 47, 6580}, {2, 4, 5, 35, 48, 1680}, {2, 4, 5,
   35, 49, 980}, {2, 4, 5, 35, 50, 700}, {2, 4, 5, 35, 52, 455}, {2,
   4, 5, 35, 55, 308}, {2, 4, 5, 35, 56, 280}, {2, 4, 5, 35, 60,
   210}, {2, 4, 5, 35, 63, 180}, {2, 4, 5, 35, 70, 140}, {2, 4, 5, 35,
    80, 112}, {2, 4, 5, 35, 84, 105}, {2, 4, 5, 36, 46, 2070}, {2, 4,
   5, 36, 48, 720}, {2, 4, 5, 36, 50, 450}, {2, 4, 5, 36, 54,
   270}, {2, 4, 5, 36, 60, 180}, {2, 4, 5, 36, 70, 126}, {2, 4, 5, 36,
    72, 120}, {2, 4, 5, 37, 44, 4070}, {2, 4, 5, 37, 45, 1332}, {2, 4,
    5, 38, 44, 1045}, {2, 4, 5, 38, 45, 684}, {2, 4, 5, 38, 76,
   95}, {2, 4, 5, 39, 42, 1820}, {2, 4, 5, 39, 45, 468}, {2, 4, 5, 39,
    52, 195}, {2, 4, 5, 39, 60, 130}, {2, 4, 5, 40, 41, 1640}, {2, 4,
   5, 40, 42, 840}, {2, 4, 5, 40, 44, 440}, {2, 4, 5, 40, 45,
   360}, {2, 4, 5, 40, 48, 240}, {2, 4, 5, 40, 50, 200}, {2, 4, 5, 40,
    56, 140}, {2, 4, 5, 40, 60, 120}, {2, 4, 5, 40, 65, 104}, {2, 4,
   5, 40, 72, 90}, {2, 4, 5, 42, 45, 252}, {2, 4, 5, 42, 56, 120}, {2,
    4, 5, 42, 60, 105}, {2, 4, 5, 42, 70, 84}, {2, 4, 5, 44, 45,
   198}, {2, 4, 5, 44, 55, 110}, {2, 4, 5, 44, 70, 77}, {2, 4, 5, 45,
   48, 144}, {2, 4, 5, 45, 52, 117}, {2, 4, 5, 45, 54, 108}, {2, 4, 5,
    45, 60, 90}, {2, 4, 5, 45, 63, 84}, {2, 4, 5, 48, 60, 80}, {2, 4,
   5, 50, 60, 75}, {2, 4, 5, 55, 60, 66}, {2, 4, 6, 13, 157,
   24492}, {2, 4, 6, 13, 158, 12324}, {2, 4, 6, 13, 159, 8268}, {2, 4,
    6, 13, 160, 6240}, {2, 4, 6, 13, 162, 4212}, {2, 4, 6, 13, 164,
   3198}, {2, 4, 6, 13, 165, 2860}, {2, 4, 6, 13, 168, 2184}, {2, 4,
   6, 13, 169, 2028}, {2, 4, 6, 13, 172, 1677}, {2, 4, 6, 13, 174,
   1508}, {2, 4, 6, 13, 180, 1170}, {2, 4, 6, 13, 182, 1092}, {2, 4,
   6, 13, 192, 832}, {2, 4, 6, 13, 195, 780}, {2, 4, 6, 13, 204,
   663}, {2, 4, 6, 13, 208, 624}, {2, 4, 6, 13, 228, 494}, {2, 4, 6,
   13, 234, 468}, {2, 4, 6, 13, 260, 390}, {2, 4, 6, 13, 273,
   364}, {2, 4, 6, 13, 300, 325}, {2, 4, 6, 14, 85, 7140}, {2, 4, 6,
   14, 86, 3612}, {2, 4, 6, 14, 87, 2436}, {2, 4, 6, 14, 88,
   1848}, {2, 4, 6, 14, 90, 1260}, {2, 4, 6, 14, 91, 1092}, {2, 4, 6,
   14, 92, 966}, {2, 4, 6, 14, 93, 868}, {2, 4, 6, 14, 96, 672}, {2,
   4, 6, 14, 98, 588}, {2, 4, 6, 14, 100, 525}, {2, 4, 6, 14, 102,
   476}, {2, 4, 6, 14, 105, 420}, {2, 4, 6, 14, 108, 378}, {2, 4, 6,
   14, 112, 336}, {2, 4, 6, 14, 120, 280}, {2, 4, 6, 14, 126,
   252}, {2, 4, 6, 14, 132, 231}, {2, 4, 6, 14, 133, 228}, {2, 4, 6,
   14, 140, 210}, {2, 4, 6, 14, 147, 196}, {2, 4, 6, 14, 156,
   182}, {2, 4, 6, 15, 61, 3660}, {2, 4, 6, 15, 62, 1860}, {2, 4, 6,
   15, 63, 1260}, {2, 4, 6, 15, 64, 960}, {2, 4, 6, 15, 65, 780}, {2,
   4, 6, 15, 66, 660}, {2, 4, 6, 15, 68, 510}, {2, 4, 6, 15, 69,
   460}, {2, 4, 6, 15, 70, 420}, {2, 4, 6, 15, 72, 360}, {2, 4, 6, 15,
    75, 300}, {2, 4, 6, 15, 76, 285}, {2, 4, 6, 15, 78, 260}, {2, 4,
   6, 15, 80, 240}, {2, 4, 6, 15, 84, 210}, {2, 4, 6, 15, 85,
   204}, {2, 4, 6, 15, 90, 180}, {2, 4, 6, 15, 96, 160}, {2, 4, 6, 15,
    100, 150}, {2, 4, 6, 15, 105, 140}, {2, 4, 6, 15, 108, 135}, {2,
   4, 6, 15, 110, 132}, {2, 4, 6, 16, 49, 2352}, {2, 4, 6, 16, 50,
   1200}, {2, 4, 6, 16, 51, 816}, {2, 4, 6, 16, 52, 624}, {2, 4, 6,
   16, 54, 432}, {2, 4, 6, 16, 56, 336}, {2, 4, 6, 16, 57, 304}, {2,
   4, 6, 16, 60, 240}, {2, 4, 6, 16, 64, 192}, {2, 4, 6, 16, 66,
   176}, {2, 4, 6, 16, 72, 144}, {2, 4, 6, 16, 80, 120}, {2, 4, 6, 16,
    84, 112}, {2, 4, 6, 17, 41, 8364}, {2, 4, 6, 17, 42, 1428}, {2, 4,
    6, 17, 44, 561}, {2, 4, 6, 17, 48, 272}, {2, 4, 6, 17, 51,
   204}, {2, 4, 6, 17, 68, 102}, {2, 4, 6, 18, 37, 1332}, {2, 4, 6,
   18, 38, 684}, {2, 4, 6, 18, 39, 468}, {2, 4, 6, 18, 40, 360}, {2,
   4, 6, 18, 42, 252}, {2, 4, 6, 18, 44, 198}, {2, 4, 6, 18, 45,
   180}, {2, 4, 6, 18, 48, 144}, {2, 4, 6, 18, 52, 117}, {2, 4, 6, 18,
    54, 108}, {2, 4, 6, 18, 60, 90}, {2, 4, 6, 18, 63, 84}, {2, 4, 6,
   19, 33, 2508}, {2, 4, 6, 19, 36, 342}, {2, 4, 6, 19, 38, 228}, {2,
   4, 6, 19, 57, 76}, {2, 4, 6, 20, 31, 930}, {2, 4, 6, 20, 32,
   480}, {2, 4, 6, 20, 33, 330}, {2, 4, 6, 20, 34, 255}, {2, 4, 6, 20,
    35, 210}, {2, 4, 6, 20, 36, 180}, {2, 4, 6, 20, 39, 130}, {2, 4,
   6, 20, 40, 120}, {2, 4, 6, 20, 42, 105}, {2, 4, 6, 20, 45, 90}, {2,
    4, 6, 20, 48, 80}, {2, 4, 6, 20, 50, 75}, {2, 4, 6, 20, 55,
   66}, {2, 4, 6, 21, 29, 812}, {2, 4, 6, 21, 30, 420}, {2, 4, 6, 21,
   32, 224}, {2, 4, 6, 21, 35, 140}, {2, 4, 6, 21, 36, 126}, {2, 4, 6,
    21, 42, 84}, {2, 4, 6, 21, 44, 77}, {2, 4, 6, 22, 27, 1188}, {2,
   4, 6, 22, 28, 462}, {2, 4, 6, 22, 30, 220}, {2, 4, 6, 22, 33,
   132}, {2, 4, 6, 22, 36, 99}, {2, 4, 6, 22, 44, 66}, {2, 4, 6, 24,
   25, 600}, {2, 4, 6, 24, 26, 312}, {2, 4, 6, 24, 27, 216}, {2, 4, 6,
    24, 28, 168}, {2, 4, 6, 24, 30, 120}, {2, 4, 6, 24, 32, 96}, {2,
   4, 6, 24, 33, 88}, {2, 4, 6, 24, 36, 72}, {2, 4, 6, 24, 40,
   60}, {2, 4, 6, 24, 42, 56}, {2, 4, 6, 25, 30, 100}, {2, 4, 6, 26,
   39, 52}, {2, 4, 6, 27, 36, 54}, {2, 4, 6, 28, 30, 70}, {2, 4, 6,
   30, 36, 45}, {2, 4, 7, 10, 141, 19740}, {2, 4, 7, 10, 142,
   9940}, {2, 4, 7, 10, 144, 5040}, {2, 4, 7, 10, 145, 4060}, {2, 4,
   7, 10, 147, 2940}, {2, 4, 7, 10, 148, 2590}, {2, 4, 7, 10, 150,
   2100}, {2, 4, 7, 10, 154, 1540}, {2, 4, 7, 10, 156, 1365}, {2, 4,
   7, 10, 160, 1120}, {2, 4, 7, 10, 165, 924}, {2, 4, 7, 10, 168,
   840}, {2, 4, 7, 10, 175, 700}, {2, 4, 7, 10, 180, 630}, {2, 4, 7,
   10, 189, 540}, {2, 4, 7, 10, 190, 532}, {2, 4, 7, 10, 196,
   490}, {2, 4, 7, 10, 210, 420}, {2, 4, 7, 10, 220, 385}, {2, 4, 7,
   10, 238, 340}, {2, 4, 7, 10, 240, 336}, {2, 4, 7, 10, 252,
   315}, {2, 4, 7, 11, 62, 9548}, {2, 4, 7, 11, 63, 2772}, {2, 4, 7,
   11, 66, 924}, {2, 4, 7, 11, 77, 308}, {2, 4, 7, 11, 84, 231}, {2,
   4, 7, 11, 110, 140}, {2, 4, 7, 12, 43, 1806}, {2, 4, 7, 12, 44,
   924}, {2, 4, 7, 12, 45, 630}, {2, 4, 7, 12, 46, 483}, {2, 4, 7, 12,
    48, 336}, {2, 4, 7, 12, 49, 294}, {2, 4, 7, 12, 51, 238}, {2, 4,
   7, 12, 54, 189}, {2, 4, 7, 12, 56, 168}, {2, 4, 7, 12, 60,
   140}, {2, 4, 7, 12, 63, 126}, {2, 4, 7, 12, 70, 105}, {2, 4, 7, 12,
    78, 91}, {2, 4, 7, 13, 42, 156}, {2, 4, 7, 13, 52, 91}, {2, 4, 7,
   14, 29, 812}, {2, 4, 7, 14, 30, 420}, {2, 4, 7, 14, 32, 224}, {2,
   4, 7, 14, 35, 140}, {2, 4, 7, 14, 36, 126}, {2, 4, 7, 14, 42,
   84}, {2, 4, 7, 14, 44, 77}, {2, 4, 7, 15, 25, 2100}, {2, 4, 7, 15,
   28, 210}, {2, 4, 7, 15, 30, 140}, {2, 4, 7, 15, 35, 84}, {2, 4, 7,
   15, 42, 60}, {2, 4, 7, 16, 24, 336}, {2, 4, 7, 16, 28, 112}, {2, 4,
    7, 16, 42, 48}, {2, 4, 7, 17, 21, 1428}, {2, 4, 7, 18, 20,
   630}, {2, 4, 7, 18, 21, 252}, {2, 4, 7, 18, 28, 63}, {2, 4, 7, 18,
   36, 42}, {2, 4, 7, 20, 21, 105}, {2, 4, 7, 20, 30, 42}, {2, 4, 7,
   21, 24, 56}, {2, 4, 7, 21, 28, 42}, {2, 4, 8, 9, 73, 5256}, {2, 4,
   8, 9, 74, 2664}, {2, 4, 8, 9, 75, 1800}, {2, 4, 8, 9, 76,
   1368}, {2, 4, 8, 9, 78, 936}, {2, 4, 8, 9, 80, 720}, {2, 4, 8, 9,
   81, 648}, {2, 4, 8, 9, 84, 504}, {2, 4, 8, 9, 88, 396}, {2, 4, 8,
   9, 90, 360}, {2, 4, 8, 9, 96, 288}, {2, 4, 8, 9, 99, 264}, {2, 4,
   8, 9, 104, 234}, {2, 4, 8, 9, 108, 216}, {2, 4, 8, 9, 120,
   180}, {2, 4, 8, 9, 126, 168}, {2, 4, 8, 9, 136, 153}, {2, 4, 8, 10,
    41, 1640}, {2, 4, 8, 10, 42, 840}, {2, 4, 8, 10, 44, 440}, {2, 4,
   8, 10, 45, 360}, {2, 4, 8, 10, 48, 240}, {2, 4, 8, 10, 50,
   200}, {2, 4, 8, 10, 56, 140}, {2, 4, 8, 10, 60, 120}, {2, 4, 8, 10,
    65, 104}, {2, 4, 8, 10, 72, 90}, {2, 4, 8, 11, 30, 1320}, {2, 4,
   8, 11, 32, 352}, {2, 4, 8, 11, 33, 264}, {2, 4, 8, 11, 40,
   110}, {2, 4, 8, 11, 44, 88}, {2, 4, 8, 12, 25, 600}, {2, 4, 8, 12,
   26, 312}, {2, 4, 8, 12, 27, 216}, {2, 4, 8, 12, 28, 168}, {2, 4, 8,
    12, 30, 120}, {2, 4, 8, 12, 32, 96}, {2, 4, 8, 12, 33, 88}, {2, 4,
    8, 12, 36, 72}, {2, 4, 8, 12, 40, 60}, {2, 4, 8, 12, 42, 56}, {2,
   4, 8, 13, 21, 2184}, {2, 4, 8, 13, 24, 156}, {2, 4, 8, 13, 26,
   104}, {2, 4, 8, 14, 19, 1064}, {2, 4, 8, 14, 20, 280}, {2, 4, 8,
   14, 21, 168}, {2, 4, 8, 14, 24, 84}, {2, 4, 8, 14, 28, 56}, {2, 4,
   8, 14, 35, 40}, {2, 4, 8, 15, 18, 360}, {2, 4, 8, 15, 20, 120}, {2,
    4, 8, 15, 24, 60}, {2, 4, 8, 15, 30, 40}, {2, 4, 8, 16, 17,
   272}, {2, 4, 8, 16, 18, 144}, {2, 4, 8, 16, 20, 80}, {2, 4, 8, 16,
   24, 48}, {2, 4, 8, 18, 24, 36}, {2, 4, 8, 20, 24, 30}, {2, 4, 8,
   21, 24, 28}, {2, 4, 9, 10, 26, 2340}, {2, 4, 9, 10, 27, 540}, {2,
   4, 9, 10, 28, 315}, {2, 4, 9, 10, 30, 180}, {2, 4, 9, 10, 36,
   90}, {2, 4, 9, 10, 40, 72}, {2, 4, 9, 10, 45, 60}, {2, 4, 9, 11,
   21, 2772}, {2, 4, 9, 11, 22, 396}, {2, 4, 9, 12, 19, 342}, {2, 4,
   9, 12, 20, 180}, {2, 4, 9, 12, 21, 126}, {2, 4, 9, 12, 22, 99}, {2,
    4, 9, 12, 24, 72}, {2, 4, 9, 12, 27, 54}, {2, 4, 9, 12, 30,
   45}, {2, 4, 9, 13, 18, 156}, {2, 4, 9, 14, 15, 1260}, {2, 4, 9, 14,
    18, 84}, {2, 4, 9, 15, 18, 60}, {2, 4, 9, 15, 20, 45}, {2, 4, 9,
   16, 18, 48}, {2, 4, 9, 18, 20, 30}, {2, 4, 9, 18, 21, 28}, {2, 4,
   10, 11, 17, 3740}, {2, 4, 10, 11, 20, 110}, {2, 4, 10, 12, 16,
   240}, {2, 4, 10, 12, 18, 90}, {2, 4, 10, 12, 20, 60}, {2, 4, 10,
   12, 24, 40}, {2, 4, 10, 13, 15, 156}, {2, 4, 10, 14, 15, 84}, {2,
   4, 10, 14, 20, 35}, {2, 4, 10, 15, 16, 48}, {2, 4, 10, 15, 18,
   36}, {2, 4, 10, 15, 20, 30}, {2, 4, 10, 15, 21, 28}, {2, 4, 11, 12,
    14, 231}, {2, 4, 11, 12, 15, 110}, {2, 4, 11, 12, 22, 33}, {2, 4,
   12, 14, 15, 35}}

586个解。

{{2, 5, 6, 8, 121, 14520}, {2, 5, 6, 8, 122, 7320}, {2, 5, 6, 8, 123,
   4920}, {2, 5, 6, 8, 124, 3720}, {2, 5, 6, 8, 125, 3000}, {2, 5, 6,
   8, 126, 2520}, {2, 5, 6, 8, 128, 1920}, {2, 5, 6, 8, 129,
   1720}, {2, 5, 6, 8, 130, 1560}, {2, 5, 6, 8, 132, 1320}, {2, 5, 6,
   8, 135, 1080}, {2, 5, 6, 8, 136, 1020}, {2, 5, 6, 8, 138, 920}, {2,
    5, 6, 8, 140, 840}, {2, 5, 6, 8, 144, 720}, {2, 5, 6, 8, 145,
   696}, {2, 5, 6, 8, 150, 600}, {2, 5, 6, 8, 152, 570}, {2, 5, 6, 8,
   156, 520}, {2, 5, 6, 8, 160, 480}, {2, 5, 6, 8, 165, 440}, {2, 5,
   6, 8, 168, 420}, {2, 5, 6, 8, 170, 408}, {2, 5, 6, 8, 180,
   360}, {2, 5, 6, 8, 184, 345}, {2, 5, 6, 8, 192, 320}, {2, 5, 6, 8,
   195, 312}, {2, 5, 6, 8, 200, 300}, {2, 5, 6, 8, 210, 280}, {2, 5,
   6, 8, 216, 270}, {2, 5, 6, 8, 220, 264}, {2, 5, 6, 9, 46,
   2070}, {2, 5, 6, 9, 48, 720}, {2, 5, 6, 9, 50, 450}, {2, 5, 6, 9,
   54, 270}, {2, 5, 6, 9, 60, 180}, {2, 5, 6, 9, 70, 126}, {2, 5, 6,
   9, 72, 120}, {2, 5, 6, 10, 31, 930}, {2, 5, 6, 10, 32, 480}, {2, 5,
    6, 10, 33, 330}, {2, 5, 6, 10, 34, 255}, {2, 5, 6, 10, 35,
   210}, {2, 5, 6, 10, 36, 180}, {2, 5, 6, 10, 39, 130}, {2, 5, 6, 10,
    40, 120}, {2, 5, 6, 10, 42, 105}, {2, 5, 6, 10, 45, 90}, {2, 5, 6,
    10, 48, 80}, {2, 5, 6, 10, 50, 75}, {2, 5, 6, 10, 55, 66}, {2, 5,
   6, 11, 24, 1320}, {2, 5, 6, 11, 30, 110}, {2, 5, 6, 12, 21,
   420}, {2, 5, 6, 12, 22, 220}, {2, 5, 6, 12, 24, 120}, {2, 5, 6, 12,
    25, 100}, {2, 5, 6, 12, 28, 70}, {2, 5, 6, 12, 30, 60}, {2, 5, 6,
   12, 36, 45}, {2, 5, 6, 13, 18, 1170}, {2, 5, 6, 13, 20, 156}, {2,
   5, 6, 14, 20, 84}, {2, 5, 6, 14, 21, 70}, {2, 5, 6, 14, 30,
   35}, {2, 5, 6, 15, 16, 240}, {2, 5, 6, 15, 18, 90}, {2, 5, 6, 15,
   20, 60}, {2, 5, 6, 15, 24, 40}, {2, 5, 6, 16, 20, 48}, {2, 5, 6,
   18, 20, 36}, {2, 5, 6, 20, 21, 28}, {2, 5, 7, 8, 32, 1120}, {2, 5,
   7, 8, 35, 280}, {2, 5, 7, 8, 40, 140}, {2, 5, 7, 8, 42, 120}, {2,
   5, 7, 8, 56, 70}, {2, 5, 7, 9, 42, 45}, {2, 5, 7, 10, 18, 630}, {2,
    5, 7, 10, 20, 140}, {2, 5, 7, 10, 21, 105}, {2, 5, 7, 10, 30,
   42}, {2, 5, 7, 12, 14, 420}, {2, 5, 7, 12, 15, 140}, {2, 5, 7, 12,
   20, 42}, {2, 5, 7, 14, 20, 28}, {2, 5, 8, 9, 16, 720}, {2, 5, 8, 9,
    18, 120}, {2, 5, 8, 9, 20, 72}, {2, 5, 8, 9, 24, 45}, {2, 5, 8,
   10, 14, 280}, {2, 5, 8, 10, 15, 120}, {2, 5, 8, 10, 16, 80}, {2, 5,
    8, 10, 20, 40}, {2, 5, 8, 10, 24, 30}, {2, 5, 8, 11, 12,
   1320}, {2, 5, 8, 12, 15, 40}, {2, 5, 8, 12, 20, 24}, {2, 5, 9, 10,
   12, 180}, {2, 5, 9, 10, 15, 45}, {2, 5, 9, 10, 18, 30}, {2, 5, 9,
   12, 18, 20}, {2, 5, 10, 12, 15, 20}}
103个解。

{{2, 6, 7, 8, 16, 336}, {2, 6, 7, 8, 21, 56}, {2, 6, 7, 8, 24,
42}, {2, 6, 7, 9, 14, 126}, {2, 6, 7, 9, 18, 42}, {2, 6, 7, 10, 12,
140}, {2, 6, 7, 10, 15, 42}, {2, 6, 7, 12, 14, 28}, {2, 6, 8, 9, 12,
   72}, {2, 6, 8, 9, 18, 24}, {2, 6, 8, 10, 12, 40}, {2, 6, 8, 10, 15,
   24}, {2, 6, 9, 10, 15, 18}}

13个解。

{{3, 4, 5, 6, 21, 420}, {3, 4, 5, 6, 22, 220}, {3, 4, 5, 6, 24,
   120}, {3, 4, 5, 6, 25, 100}, {3, 4, 5, 6, 28, 70}, {3, 4, 5, 6, 30,
    60}, {3, 4, 5, 6, 36, 45}, {3, 4, 5, 7, 14, 420}, {3, 4, 5, 7, 15,
    140}, {3, 4, 5, 7, 20, 42}, {3, 4, 5, 8, 11, 1320}, {3, 4, 5, 8,
   12, 120}, {3, 4, 5, 8, 15, 40}, {3, 4, 5, 8, 20, 24}, {3, 4, 5, 9,
   10, 180}, {3, 4, 5, 9, 12, 45}, {3, 4, 5, 9, 18, 20}, {3, 4, 5, 10,
    12, 30}, {3, 4, 5, 10, 15, 20}, {3, 4, 6, 7, 10, 140}, {3, 4, 6,
   7, 12, 42}, {3, 4, 6, 7, 14, 28}, {3, 4, 6, 8, 9, 72}, {3, 4, 6, 8,
    10, 40}, {3, 4, 6, 8, 12, 24}, {3, 4, 6, 9, 12, 18}, {3, 4, 6, 10,
    12, 15}}
27个解。

总计1591+586+103+13+27=2320个解。

葡萄糖 发表于 2019-9-21 09:47:38

本帖最后由 葡萄糖 于 2019-9-21 09:53 编辑

【强烈建议管理员改一下标题】（方便以后搜索）
比如：埃及分数互异正整数解及其组数
A006585
Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
1, 0, 1, 6, 72, 2320, 245765, 151182379, ⋅⋅⋅⋅⋅⋅

查看完整版本: 连分数的难题